Real part Of Complex Numbers, Imaginary Part Of A Complex Number, Division Of Complex Numbers, complex numbers lectures, complex numbers 11th class, complex numbers IIT-JEE, complex numbers JEE, complex numbers IIT, complex numbers And Quadratic Equations, 11th Class mathematics, JEE Mathematics, IIT-JEE Mathematics, AIEEE Mathematics, PET Mathematics, CBSE Mathematics, 11th class mathematics lectures, Imaginary numbers, real numbers, non-real numbers, multiplicative inverse of complex numbers, square root of complex numbers, complex numbers formula, 11th grade mathematics, separation of real part and imaginary part of complex numbers, problems on complex numbers, Complex numbers ncert, Concept Of Iota, Modulus, Representation, Argument(Amplitude), Inverse, Conjugate Of Complex Numbers, De-Movire's theorem, cube root of unity

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sardanatutorials

Check out Fematika's channel: https://www.youtube.com/channel/UCIUPBxtBMQvssqSbx73t8SQ
cube root of i,
cbrt(i),
i^(1/3),
some complex analysis,
blackpenredpen,
math for fun,

Views: 42893
blackpenredpen

For more Information & Topic wise videos visit: www.impetusgurukul.com
I hope you enjoyed this video. If so, make sure to like, comment, Share and Subscribe!

Views: 33898
Impetus Gurukul

If you like this video and want to support me, go this page for my donation crypto addresses:
https://www.youtube.com/c/mobilefish/about
This is part 2 of the IOTA tutorial.
In this video series different topics will be explained which will help you to understand IOTA.
It is recommended to watch each video sequentially as I may refer to certain IOTA topics explained earlier.
The trinary numeral system has two types:
The balanced trinary system in which a trit has the values -1, 0 and 1.
The unbalanced trinary system in which a trit has the values 0, 1 and 2.
In this presentation I will only focus on the balanced trinary system.
Trit means Trinary Digit, analogous to bit and has the following values: -1, 0 and 1.
Tryte means Trinary Byte, analogous to byte.
A tryte consists of 3 trits.
1 byte = 2^8 = 256 combinations
1 tryte = 3 trits = 3^3 = 27 combinations
5 trits = 3^5 = 243 combinations
5 trits is NOT equal to 1 byte
Convert tryte -1, 1, 0 to integer:
-1 x 3^0 + 1 x 3^1 + 0 x 3^2 = 2
Convert tryte 1, -1, 1 to integer:
1 x 3^0 + -1 x 3^1 + 1 x 3^2 = 7
What is the maximum value a tryte can have (not the number of combinations)?
Answer: 13
If you thought 3^3 - 1 = 26 you are thinking in the binary system.
If you have 2 bits in a binary system, you have the following combinations:
00 = 0x2^1 + 0x2^0 = 0
01 = 0x2^1 + 1x2^0 = 1
10 = 1x2^1 + 0x2^0 = 2
11 = 1x2^1 + 1x2^0 = 3
Max value = 2^2 - 1
If you have 2 trits in a balanced trinary system, you have the following combinations:
0, 0 = 0x3^0 + 0x3^1 = 0
0, 1 = 0x3^0 + 1x3^1 = 3
0,-1 = 0x3^0 + -1x3^1 = -3
1, 0 = 1x3^0 + 0x3^1 = 1
1, 1 = 1x3^0 + 1x3^1 = 4
1,-1 = 1x3^0 + -1x3^1 = -2
-1, 0 = -1x3^0 + 0x3^1 = -1
-1, 1 = -1x3^0 + 1x3^1 = 2
-1,-1 = -1x3^0 + -1x3^1 = -4
The values in the trinary system are balanced around zero:
-4, -3, -2, -1, 0, 1, 2, 3, 4
Max value = (3^2 - 1) / 2
A tryte has 3 trits, so the maximum value will be (3^3 -1) / 2 = 13 and it has 3^3 = 27 combinations.
A tryte will have the following values: -13, -12, …-2, -1, 0, 1, 2,...12, 13
Convert the following two trytes -1, -1, -1, 1, 0, 0 to an integer:
-1 x 3^0 + -1 x 3^1 + -1 x 3^2 + 1 x 3^3 + 0 x 3^4 + 0 x 3^5
-13 + 27 = 14
IOTA uses the balanced trinary system
To make the trytes more human readable the IOTA development team created the tryte alphabet:
9ABCDEFGHIJKLMNOPQRSTUVWXYZ
The tryte alphabet consists of 26 letters of the latin alphabet plus the number 9.
The tryte alphabet has a total of 27 characters.
Because 1 tryte has 3^3 = 27 combinations, each tryte can be represented by a character in the tryte alphabet.
Tryte alphabet:
Tryte Dec Char
0, 0, 0 0 9
1, 0, 0 1 A
-1, 1, 0 2 B
0, 1, 0 3 C
1, 1, 0 4 D
-1,-1, 1 5 E
0,-1, 1 6 F
1,-1, 1 7 G
-1, 0, 1 8 H
0, 0, 1 9 I
1, 0, 1 10 J
-1, 1, 1 11 K
0, 1, 1 12 L
1, 1, 1 13 M
-1,-1,-1 -13 N
0,-1,-1 -12 O
1,-1,-1 -11 P
-1, 0,-1 -10 Q
0, 0,-1 -9 R
1, 0,-1 -8 S
-1, 1,-1 -7 T
0, 1,-1 -6 U
1, 1,-1 -5 V
-1,-1, 0 -4 W
0,-1, 0 -3 X
1,-1, 0 -2 Y
-1, 0, 0 -1 Z
IOTA seeds, addresses, hashes, etc are trytes which are represented by characters from the tryte alphabet.
For example the integer 14, converted into trytes: -1, -1, -1, 1, 0, 0
Convert the trytes using the tryte alphabet:
-1, -1, -1 = N
1, 0, 0 = A
Thus integer 14 converted into trytes: NA
The word “Zoo” converted into trytes looks like: ICCDCD
The ASCII value of Z = 90, converted to trytes: 0,0,1,0,1,0 = IC
The ASCII value of o = 111, converted to trytes: 0,1,0,1,1,0 = CD
An IOTA seed contains 81 characters which is the same as 81 trytes.
For example: C9RQFODNSAEOZVZKEYNVZDHYUJSA9QQRCUJVBJD9KHAKPTAKZSNNKLJHEFFVK9AWVDAUJRYYKHGWQIAWF
Each tryte has 27 combinations, which means an IOTA seed has:
27^81 = ~8.71 x 10^115 combinations
In comparison a Bitcoin random number has:
2^256 = ~1.15 x 10^77 combinations
Check out all my other IOTA tutorial videos
https://goo.gl/aNHf1y
Subscribe to my YouTube channel:
https://goo.gl/61NFzK
The presentation used in this video tutorial can be found at:
https://www.mobilefish.com/developer/iota/iota_quickguide_tutorial.html
#mobilefish #howto #iota

Views: 10928
Mobilefish.com

To Ask Unlimited Math Doubts From Class 6-12, JEE Mains and advanced, Download Doubtnut From - https://doubtnut.app.link/Y2v8kXcguO
complex^complex=real? or Imaginary ? or New kind of numbers ?
what is i^i ?
What iota to power iota Represents ?
i^i,
e^(-pi/2),
classic math problem,
complex exponent,
polar form of complex numbers,

Views: 1074
Doubtnut

To ask any doubt in Math download Doubtnut: https://goo.gl/s0kUoe
Question: 18. (i z)(1 +2i) (1 iz) (3-4) 1 +7i z 3 102 58 136 0.

Views: 108
Doubtnut

Type 0.5! in your calculator to see what the factorial of one-half is. The result will be 0.886..., and the exact answer is the square root of pi divided by 2--amazing! How is this possible, when the factorial of a number n is defined as n! = n(n-1)(n-2)...1 and this definition only makes sense for whole numbers?
The calculator result is not an error, and in this video I explain how the factorial can be extended beyond the whole numbers for all real numbers by the gamma function. Once we extend the factorial function beyond whole numbers, you can see why the factorial of one-half is equal to the square root of pi divided by 2.
Bohr-Mollerup theorem
http://en.wikipedia.org/wiki/Bohr%E2%80%93Mollerup_theorem
Applications
https://www.math.washington.edu/~morrow/336_10/papers/joel.pdf
Numerical computation
http://www.rskey.org/CMS/index.php/the-library/11
Alternative ways to extend the factorial function
http://www.luschny.de/math/factorial/hadamard/HadamardsGammaFunctionMJ.html
If you like my videos, you can support me at Patreon:
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My Books
"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.9/5 stars on 32 reviews)
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"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews.
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"Math Puzzles Volume 2" is a sequel book with more great problems. (rated 4.3/5 stars on 4 reviews)
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"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews)
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Views: 859271
MindYourDecisions

For this Christmas video the Mathologer sets out to explain Euler's identity e to the pi i = -1, the most beautiful identity in math to our clueless friend Homer Simpson. Very challenging to get this right since Homer knows close to no math!
Here are a couple of other nice videos on Euler's identity that you may want to check out:
https://youtu.be/Yi3bT-82O5s (one of our Math in the Simpsons videos)
https://youtu.be/F_0yfvm0UoU (by 3Blue1Brown)
And for those of you who enjoy some mathematical challenges here is your homework assignment on Euler's identity:
1. How much money does Homer have after Pi years if interest is compounded continuously?
2. How much money does Homer have after an imaginary Pi number of years?
3. As we've seen when you let m go to infinity the function (1+x/m)^m turns into the exponential function. In fact, it turns into the infinite series expansion of the exponential function that we used in our previous video. Can you explain why?
4. Can you explain the e to pi i paradox that we've captured in this video on Mathologer 2: https://youtu.be/Sx5_QGdFmq4.
If you own Mathematica you can play with this Mathematica notebook that I put together for this video
http://www.qedcat.com/misc/Mathologer_eipi.nb
Thank you very much to Danil Dmitriev the official Mathologer translator for Russian for his subtitles.
Merry Christmas!
Burkard Polster

Views: 1702192
Mathologer

This is a quick tutorial that will help you to find the square root of iota ( square root of i ).
There will two values of square root (i), like the square root of any real number.
* Iota is a greek letter which is widely used in mathematics to denote the imaginary part of a complex number. Let's say we have an equation: x^2 + 1 = 0 . In this case, the value of x will be the square root of -1, which is fundamentally not possible.
The term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero, which has one double square root.
Unit Imaginary Number. The "unit" Imaginary Number (the equivalent of 1 for Real Numbers) is √(−1) (the square root of minus one). In mathematics we use i (for imaginary) but in electronics they use j (because "i" already means current, and the next letter after i is j).
==================================
Music: https://www.youtube.com/watch?v=K8eRXvLL7Wo
==================================
Social touch:-
Twitter: https://twitter.com/Pefcoy
==================================

Views: 1294
pefcoy

polar way: https://youtu.be/Y7su8b8v0i0
Please subscribe for more calculus tutorials and share my videos to help my channel grow! 😃
T-shirt: https://teespring.com/derivatives-for-you
Patreon: https://www.patreon.com/blackpenredpen
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sqrt(i),
sqrt(i) as a complex number,
www.blackpenredpen.com,
math for fun,

Views: 595818
blackpenredpen

Views: 780
easy math & phy

It might seem odd to need to find the square root of a complex number. However, the square root of a complex number is just as valid a mathematical calculation as find the square root of a real number. The process I show here is very simple and is one of several mathematically equivalent methods.

Views: 2670
purdueMET

How to use scientific calculator to calculate square root of complex numbers. Trick in Hindi.

Views: 5679
RF Design Basics

This video describes about the cube roots of unity. In mathematics, a root of unity, occasionally called a De Moivre number, is any complex number that equals 1 when raised to some integer power n. Roots of unity are used in many branches of mathematics, and are especially important in number theory, the theory of group characters, field theory, and the discrete Fourier transform.

Views: 37667
XLClasses

I created this video using my Logitech webcam software.

Views: 1621
C A Beverforden

We know what Real Numbers are. But what about Imaginary numbers? Do they exist? Who discovered them? Watch this video to know the answers. To view the entire course, visit https://dontmemorise.com/course/index.php?categoryid=40
Don’t Memorise brings learning to life through its captivating FREE educational videos. To Know More, visit https://DontMemorise.com
New videos every week. To stay updated, subscribe to our YouTube channel : http://bit.ly/DontMemoriseYouTube
Register on our website to gain access to all videos and quizzes:
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Views: 167306
Don't Memorise

Sound quality is bit low but i will try to overcome this problem as soon as possile
Keep wathching
And keep sharing
Thank you

Views: 138
ayush prasad shaw

Imaginary numbers also known as Complex numbers are the numbers that cannot be represented on the real number line.
The video is only an introduction to the number we'll be making more on the topic so stay tuned.
The idea of imaginary numbers was first given by Gerolamo Cardano. He was a Italian mathematician.
Iota is the square root of negative of one which cannot be represented on the real number line.
If you want quality study material for physics for class 9th, 10th, 11th or 12th you can visit the following website
http://www.vkphysics.wordpress.com
And follow me on instagram.
https://www.instagram.com/harshitrawat70/
And don't forget to like and subscribe and sharing is must.
Song used : The long road home - Inukshuk (NCS release)

Views: 116
Physicmatics HR

Watch My Other Calculator Tutorials Below-
http://goo.gl/uiTDQS
Today I'll tell you about 20 cool features of Casio fx-82MS scientific calculator.
Below is the complete list of 20 features of Casio fx-82MS and start timing of each feature in the video is given in parenthesis().
1. Settings Up Your Casio fx-82MS Calculator-
i) Meaning of SVPAM
ii) Fix function
iii) Sci function
iv) Norm1 and Norm2 function
v) Setting up display contrast of calculator
vi) Setting up default angle unit of calculator
2. Fractional Calculations on Casio fx-82MS (3:26)-
22/15 + 3/5 = 2[1/15] = 31/15
3. Percentage Calculations on Casio fx-82MS (3:58)-
What percent is 126 of 700 ?
Increase 540 by 15% ?
Discount 324 by 25% ?
Increase in percentage if 40 increased to 46 ?
4. Sexagesimal(Hour-Minute-Second) Calculations on Casio fx-82MS (6:21)-
2hr 20min 30sec + 0hr 39min 30sec = ?
5. Multi Statement Calculations on Casio fx-82MS (6:50)-
10/3 + 8/3 : 9/3 = ?
6. Calculator Memories on Casio fx-82MS (7:47)-
i) Replay Memory
ii) Answer memory
iii) Clearing the memories
7. Using Memory Variables(A,B,C,D,E,F,X,Y) on Casio fx-82MS (8:41)-
8. Random Number Generator on Casio fx-82MS (9:22)-
9. Sin,Cos,Tan Trigonometric Functions on Casio fx-82MS (9:52)-
10. Factorial(!) Calculations on Casio fx-82MS (10:47)-
11. Permutations on Casio fx-82MS (11:01)-
12. Combinations on Casio fx-82MS (11:23)-
13. Squaring and n-th root on Casio fx-82MS (11:43)-
Squaring,Cube,Square root,Cube root,n-th power,n-th root.
14. Using Independent Memory(M) on Casio fx-82MS (12:35)-
15. Rectangular to Polar Coordinate Conversion on Casio fx-82MS (13:19)-
16. Polar To Rectangular Coordinate Conversion on Casio fx-82MS (14:00)-
17. Scientific Constants(Euler Number & Pi) on Casio fx-82MS (14:33)-
18. Logarithmic Calculations(log & ln) on Casio fx-82MS (15:03)-
19. Hyperbolic Functions(Sinh,Cosh,Tanh) on Casio fx-82MS (15:19)-
20. Conversions Between Degree,Radian & Gradient on Casio fx-82MS (15:37)-
I've uploaded videos on Statistics,Numerical Methods,
Business & Financial Mathematics,Operations Research,Computer Science,Electrical Engineering,Android Application Reviews,India Travel & Tourism,Street Foods,Life Hacks and many other topics.
And a series of videos showing how to use your scientific calculators Casio fx-991ES & fx-82MS to do maths easily.
Join me at my YouTube Channel- http://www.youtube.com/sujoyn70
Join me at my Blog- http://www.sujoyn70.blogspot.com

Views: 348212
Sujoy Krishna Das

Integral power of iota i. Problems Based On iota in Complex Numbers.
Play List of Complex Numbers | Class-11 CBSE/JEE Mains & Advanced ( 51 FULL Chapter Videos )
https://www.youtube.com/playlist?list=PLI3BX4bvdDGqx1fvfbrBF8UEKW0Z0w07i
MATHSkart.in is Online Tutorial Video For IIT-JEE Students who wants Complete Chapter wise syllabus of MATHS for MAINS and ADVANCED of IIT- JEE, FREE of Cost on YOU TUBE.
BPS Chauhan is Senior MATHS Faculty who belongs to KOTA only having more than 21 years of Experience. He worked with RESONANCE, NARAYANA, CAREER POINT and ALLEN institute.
KOTA style of Teaching now available on www.mathskart.in through YouTube and available complete chapter wise syllabus of MATHS for JEE aspirants students.
MATHSkart is committed to provide VIDEOS for 9, 10, 11 and 12 CBSE/NTSE /Olympiad Level also.
Main features of our Video Lectures to Provide HD Videos of Real Class Room feel with Important Examples solution.
MATHSkart extends his hands to Provide FREE Lectures for those economically poor students who are unable to come KOTA but wants Coaching of KOTA FREE OF COST.
http://www.mathskart.in
https://web.facebook.com/?_rdc=1&_rdr
https://www.linkedin.com/in/bhupendra-pal-singh-chauhan-3171604b/
https://twitter.com/BpsKota
https://www.instagram.com/?hl=en
https://www.quora.com/profile/Bhupendra-Pal-Singh-Chauhan #MATHSkart

Views: 5190
mathskart By BPS Chauhan

In This Video iota (i) is proved equals to unity. But there is a Mathematical error to prove it. Please comment in which step there is error.

Views: 439
My Dear Maths

I created this video with the YouTube Video Editor (http://www.youtube.com/editor) this vedio is cc type vedio

Views: 4106
eSmart Classes

Views: 176
ayush prasad shaw

Multiplicative Inverse of Iota - Iota is imaginary unit of every complex number. Iota is a greek symbol given by Mathematician Euler. Square of iota is equal to - 1. In this Complex Number Exercise we are finding the multiplicative inverse of the iota. To find the multiplicative of iota again we have two choice one by using formula which is generally fast and another method to find the multiplicative inverse of iota is manual, just by multiplying and dividing by the conjugate of the complex number after writing it into the multiplicative inverse form.
I hope this video will give you proper guide to write the multiplicative inverse of complex number.

Views: 1997
IMA Videos

This video shows you how to find all real and imaginary solutions or rational zeros / roots of a polynomial function / equation by factoring, using the quadratic equation or even using synthetic division.

Views: 68539
The Organic Chemistry Tutor

This video will let you find the sqrt of any complex number which is not natively supported by Casio fx-991es/plus.
In this video I have used a small algorithm to calculated the aforementioned, which is as follows:
1. Take the number in a+ib format whose sqrt you have to find.
2. Convert the number with a+ib format into rLθ.
3. We will now find the sqrt of r and Lθ separately.
4. For finding sqrt of r simply take its sqrt.
5. For finding the sqt of Lθ divide the angle by 2.
(Remember that sqrt, cube root, quad root of angle are found by
dividing them accordingly by 2, 3, 4 respectively.)
6. Now you have the result for sqrt in rLθ format.
7. Again convert it into a+ib form.
Please do subscribe for more upcoming tutorials.

Views: 36676
Mohit Sims Mishra

6 JEE Advanced Level solved questions and Chapter analysis with Karthik Sir.
Complex numbers build from the concepts of quadratic equations. Every concept here is new. We begin by looking at iota and its properties, look at complex numbers and their equality, modulus, argument and conjugate of complex numbers. The different forms of a complex number are of great interest with focus on the polar form. de Moivre's theorem which builds on to concepts such as roots of the complex number and cube root of unity are applied primarily to the polar form. Representation of geometrical figures on the complex (argand) plane concludes this rather interesting chapter. From the JEE point of view, this chapter is quite relevant as questions regularly appear from this chapter in the exams. Also, it is interesting to note that, though the name of the chapter has complex in it, the questions from here are not very convoluted. We will be exploring these topics and the questions from them in this video.
Question 1: In this video, we make use of the properties of iota. Using the values of iota when raised to certain powers we evaluate the summation of iota raised to powers ranging from 0 to 100!. 07:15
Question 2: In this video, we look into a number of concepts involving the argument of a complex number. We look at the properties of the argument of the product of two complex numbers and the argument of the conjugate of a complex number. Also, the arguments of the conjugate of complex numbers in different quadrants are illustrated graphically. 10:38
Question 3:
This video deals with the properties of real and complex roots of a polynomial. Using the value of cube roots of unity we find the degree of a given polynomial with real coefficients, four of whose roots are given. We utilise the property that the complex roots of a polynomial always exist in conjugate pairs. 14:00
Question 4:This video utilities the property of modulus of a complex number to solve a given equation in complex numbers. Using the expression for the modulus of a complex number we simplify an equation in complex numbers using the concept of equality of a complex number. Further different cases to be considered while solving an absolute value equation are also illustrated. 18:48
Question 5: Equality of a complex number is explored using the polar form of a complex number. The concept of AM ≥ GM is illustrated while solving the equality of real and imaginary parts of the complex number. Further, de Moivre’s theorem is used to raise the complex number to the thousandth power. The solution to the question is completed using the concepts of trigonometric ratios of angles in various quadrants.24:26
Question 6: This video shows the representation of a given complex number in the Argand Plane. We make use of the complex number representation of circles to begin the solution to the question. Further, utilizing the properties of the transformations such as translation and dilation of complex numbers in the Argand Plane, we find the locus of a given complex number. This question is completely solved graphically without resorting to algebraic manipulations. 29:23
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Views: 5835
BYJU'S JEE

Given an integer, how do you find the square root of the number without using any built-in function?
If the number is not a perfect square then take precision = 0.0005.
The number can be a positive or negative integer.
Example:
Square root of 1024 = 32
Square root of 2 = 1.41455078125
Square root of -256 = 16i (i = iota = √-1)
Algorithm:
The algorithm uses Binary Search.
Initialize start = 0 and end = number.
At every step, we find out the mid value from start and end and then check if it is the square root (in case the number is perfect square) or whether we are reaching the square root within give precision by comparing current mid value to previous mid value (in case the number is not a perfect square).
1. Initialize, start = 0, end = number, mid = (start+end)/2.
2. Set prevMid = 0, as the previous mid value.
3. Find diff = absolute difference between prevMid and mid.
4. While mid is not the square root of number (i.e. mid*mid != number) and difference diff is greater than 0.0005, repeat the following steps: a. If mid*mid is greater than number, then the square root will be less than mid. So, set end = mid.
b. Else, the square root will be greater than mid. So, set start = mid. c. Set prevMid = mid
d. Re-evaluate mid = (start+end)/2.
e. Re-evaluate diff from prevMid and mid.
If the given number is negative, then square root of the number will be square root of positive part of the number * i (iota).
For example:√-256 = √256 * √-1 = 16i
Code and Algorithm Visualization:
http://www.ideserve.co.in/learn/square-root-of-a-number
Website: http://www.ideserve.co.in
Facebook: https://www.facebook.com/IDeserve.co.in

Views: 9597
IDeserve

This algebra 1 & 2 introduction video tutorial shows you how to add and subtract complex numbers, how to multiply and divide imaginary numbers in addition to graphing and solving equations with complex numbers. Examples include the following topics:
Simplifying complex imaginary numbers:
i^7, i^11, i^15, i^303
Adding and Subtracting Complex Numbers:
(4+3i) + (2+5i)
8(2+5i)-3(4-7i)
Multiplying Imaginary Numbers:
(3+7i)(2-5i)
Dividing Complex Numbers: (using the conjugate of the denominator / rationalizing)
(3+2i)/(5-3i)
7/(5+i)
Solving Equations Involving Complex Imaginary Numbers:
3x + 5i = 9 + 2oyi
x^2 + 25 = 0
Graphing Complex Numbers:
3 + 2i and 2 - 4i

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The Organic Chemistry Tutor

How to find square root of complex number | in hindi

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The Dynamic TV

To ask Unlimited Maths doubts download Doubtnut from - https://goo.gl/9WZjCW If `omega` is an imaginary cube root of unity, then find the value of `(1+omega)(1+omega^2)(1+omega^3)(1+omega^4)(1+omega^5)........(1+omega^(3n))=`

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Doubtnut

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Impetus Gurukul

Real part Of Complex Numbers, Imaginary Part Of A Complex Number, Division Of Complex Numbers, complex numbers lectures, complex numbers 11th class, complex numbers IIT-JEE, complex numbers JEE, complex numbers IIT, complex numbers And Quadratic Equations, 11th Class mathematics, JEE Mathematics, IIT-JEE Mathematics, AIEEE Mathematics, PET Mathematics, CBSE Mathematics, 11th class mathematics lectures, Imaginary numbers, real numbers, non-real numbers, multiplicative inverse of complex numbers, square root of complex numbers, complex numbers formula, 11th grade mathematics, separation of real part and imaginary part of complex numbers, problems on complex numbers, Complex numbers ncert, Concept Of Iota, Modulus, Representation, Argument(Amplitude), Inverse, Conjugate Of Complex Numbers, De-Movire's theorem, cube root of unity

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sardanatutorials

To ask any doubt in Math download Doubtnut: https://goo.gl/s0kUoe
Question: Simplify and express the result in the form (a+ib): (i) (3+sqrt(-16))-(4-sqrt(-9)) (ii) (7-5i)(3+i)

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Doubtnut

To ask Unlimited Maths doubts download Doubtnut from - https://goo.gl/9WZjCW If `omega` is the complex cube root of unity, then prove that `|[1,1,1],[1,-1-omega^2,omega^2],[1,omega^2,omega^4]|=+-3sqrt3i`

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Doubtnut

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Finding roots of complex numbers. Here I give the formula to find the n-th root of a complex number and use it to find the square roots of a number.

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patrickJMT

In this video, we have studied how to solve a problem involving iota (denoted by i). The imaginary number i is defined solely by the property that its square is −1. Many mathematical operations that can be carried out with real numbers can also be carried out with i, such as exponentiation, roots, logarithms, and trigonometric functions.
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Basic concepts of Complex cube roots of unity and their properties

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mathematicaATD

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Modulus Of Complex Number. Absolute Value Of Complex Number. Properties of Modulus of Complex Numbers With Proof. Geometrical Interpretation of Modulus of Complex Numbers.
Play List of Complex Numbers | Class-11 CBSE/JEE Mains & Advanced ( 51 FULL Chapter Videos )
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Complex Numbers
Cube Roots of Unity
Third Property: The Product of all three cube roots of unity is Unity.
i.e, 1.ω.ω^2=ω^3=1
Proof:
We know that cube root of unity are
Where ω=(-1+√3 i)/2 and ω^2=(-1-√3 i)/2
Product of all the three cube roots:
1.ω.ω^2=1 Equation no.1
Put values of ω and ω^2in above equation,
1.ω.ω^2= 1.(-1+√3 i)/2.(-1-√3 i)/2
Using Formula of a^2-b^2=(a+b)(a-b) where
a=-1 and b=√3 i)
=((-1)^2-(√3 i)^2)/4=(1-(-3))/4 as i^2=-1
=(1+3)/4=4/4=1
Hence Product of cube roots of unity = 1.ω.ω^2=ω^3=1

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Mathematics with c language

Video Lecture on Example 3 of Integral Power of iota(i) from Complex Numbers chapter of IIT JEE Mathematics Video Tutorials, Video Lectures for all aspiring Students to Study IIT JEE Mathematics.
Watch Previous Videos of Chapter Complex Numbers:-
1) Integral Power of iota(i) - Example 1 - Complex Numbers - IIT JEE Mathematics Video Lectures - https://youtu.be/PRXioLJMM3c
2) Integral Power of iota(i) - Example 2 - Complex Numbers - IIT JEE Mathematics Video Lectures - https://youtu.be/FM-68aQkndc
Watch Next Videos of Chapter Complex Numbers:-
1) Integral Power of iota(i) - Example 4 - Complex Numbers - IIT JEE Mathematics Video Lectures - https://youtu.be/KlTWXtYdSk4
2) Equality of Complex Numbers - Complex Numbers - IIT JEE Mathematics Video Lectures - https://www.youtube.com/watch?v=imIdpwDxzhA
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Ekeeda

we learnt about iota which is a complex number equal to i= √(−1) Now, can we find power of iota (in) when n is any whole number. Lets simply calculate some of them and then I will define some general rule.
its an imaginary number equal to square root of -1. It is used in comlex numbers which have both real part and an imaginary part. The representaion of a complex number Z is given as Z=a+ib, where a is real part and b is the imaginary part. and i represents iota. Its use in mathematics is to obtaining solutions of equations which seem to have no real solution. To bypass this limit of not being able t osolve equation with no real solutions , the concept of imaginary or complex numbers evolved. However, its significance in real world is that it helps you to reduce the number of solutions of a equation of Nth degree to N-k if it has k imaginary roots.

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Mathematics Guru R.K Shrivastava

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intrepid Geeks

Real part Of Complex Numbers, Imaginary Part Of A Complex Number, Division Of Complex Numbers, complex numbers lectures, complex numbers 11th class, complex numbers IIT-JEE, complex numbers JEE, complex numbers IIT, complex numbers And Quadratic Equations, 11th Class mathematics, JEE Mathematics, IIT-JEE Mathematics, AIEEE Mathematics, PET Mathematics, CBSE Mathematics, 11th class mathematics lectures, Imaginary numbers, real numbers, non-real numbers, multiplicative inverse of complex numbers, square root of complex numbers, complex numbers formula, 11th grade mathematics, separation of real part and imaginary part of complex numbers, problems on complex numbers, Complex numbers ncert, Concept Of Iota, Modulus, Representation, Argument(Amplitude), Inverse, Conjugate Of Complex Numbers, De-Movire's theorem, cube root of unity

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