SOLUTION: Find three cube roots for the complex number. Leave your answers in trig form. In degrees, not cis form 8(cos 90° + i sin 90°) W0 = W1= W2=?

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Question 1080026: Find three cube roots for the complex number. Leave your answers in trig form. In degrees, not cis form 8(cos 90° + i sin 90°) W0 = W1= W2=?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
W0 = 2*(cos(30°) + i*sin(30°)).


W1 = 2*(cos(150°) + i*sin(150°)).     Notice that 150° = 30° + 120° = 30° + 360%5E0%2F3.


W1 = 2*(cos(270°) + i*sin(270°)).     Notice that 270° = 30° + 2*120° = 30° + 2%2A%28360%5E0%2F3%29.


There is a bunch of lessons on complex numbers
    - Complex numbers and arithmetical operations on them
    - Complex plane
    - Addition and subtraction of complex numbers in complex plane
    - Multiplication and division of complex numbers in complex plane
    - Raising a complex number to an integer power
    - How to take a root of a complex number (*)
    - Solution of the quadratic equation with real coefficients on complex domain
    - How to take a square root of a complex number
    - Solution of the quadratic equation with complex coefficients on complex domain

    - Solved problems on taking roots of complex numbers (*)
    - Solved problems on arithmetic operations on complex numbers
    - Solved problem on taking square root of complex number
in this site.


In this list, the lessons marked by (*) specially relate to taking roots of high degree of complex numbers.
So, these lessons specially relate to your problem.


Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Complex numbers".



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find three cube roots for the complex number. Leave your answers in trig form. In degrees, not cis form 8(cos 90° + i sin 90°)
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W1+=+root%283%2C8%29cis%2830%29
W2+=+root%283%2C8%29cis%28150%29
W3+=+root%283%2C8%29cis%28270%29
---------
Change to trig form if you like.