Exponential form to find complex roots | Imaginary and complex numbers | Precalculus | Khan Academy

Using exponential form to find complex roots

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[cpanati]

Connect the 3 roots for X^3 = 1 and you get a triangle.  Connect the 4 roots for X^4 = 1 and you get a square.  Connect the 5 roots of X^5 = 1 and you get a pentagon.  The 6 roots for X^6 = 1 and you get a hexagon.  Heptagon, Octagon, et.  You are now seeing the symmetry that leads into the subject of Group Theory.

[ctalin]

Man, it's 2 a.m. before a test and here you are! Saving my ass again, as you always did. I can't find the words to thank you enough! 

[Crossfire]

I find the repetition helps instil the information, gives myself time to get his point before he moves on. Thumbs up for every vid man, no one does this as good as you.

[philipbernstein]

man, i was struggling with this in math all last week, and you made it crystal clear to me in ten minutes....great job

[PercentageSign]

this video is golden for EE if you never get taught this until it's too late, thank you so much

[zanepotts]

I learned in 10 minutes what I had been trying to learn through an entire hour and half lecture. Thanks man!!!

[ImAllInNow]

Think in Tau, even more easy. 2 pi / 3 becomes tau/3 which is so obviously 1/3 of a full rotation.

[trbone]

That’s how 2pi/3 is expressed in complex numbers. cos(2pi/3) corresponds to the real part of the number because the real axis is horizontal and the cosine of an angle gives you the horizontal component. sin(2pi/3) corresponds to the imaginary part of the number because the imaginary axis is vertical and the sine of an angle gives you the vertical component. cos(2pi/3) (real) is -1/2 and sin(2pi/3) (imaginary) is sqrt(3)/2 (basic trig), so the complex number can be written as -1/2 + i*sqrt(3)/2.

[katherinemays]

This is probably the coolest thing I've ever seen.

[dhinas]

Well, I am not in a hurry or before a test, but i find this also nice. The explanations are so organic. Nothing stale...

[chickmagnent]

You are GREAT!!! My math teacher is good but I cannot pay attention in class, this is the solution to my problem.

[yakashgoyal]

To find the roots just use the eqn
Cosx + isinx = e^ix

[Hazit]

this guy makes me enjoy maths. my teacher can do one.lol

[boxxer]

Probably my favorite piece of maths. All maths should be this nice.

[TheNetkrot]

this was nothing but great Mr Khan ... thank you so much.

[gatlatwal]

Please help me calculate this
Given that (√3-i) is a square root of the equation Z^9+16(1+i)z^3+a+ib=0
What is the value of a and b?

[AstroKedde]

thanks i get it now :) my text book is not very good at passing on its knowledge to me and i "missed "the lecture my professors gave me on the subject..

[ItsGazareth]

He calculates the cosine and sine terms from the line above.

[paulwood]

Complex exponentials are truly amazing 👏👏👍👍

[PandorasBox]

man you are miracle worker i was so confused about this before thank you you got it all covered in less than 12 mins lol tnX again