SOLUTION: Let z = 5 + 5sqrt(3)i, Write z in polar form. Find the complex number z^9.

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Question 1131219: Let
z = 5 + 5sqrt(3)i,
Write z in polar form.
Find the complex number
z^9.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


z+=+5%2B%285%2Asqrt%283%29%29i

abs%28z%29+=+sqrt%28%285%5E2%29%2B%285%2Asqrt%283%29%29%5E2%29+=+10
theta+=+tan%5E%28-1%29%285%2Asqrt%283%29%2F5%29+=+pi%2F3

z+=+10%2Acis%28pi%2F3%29

(Note that, alternatively, you can find the magnitude and the angle by recognizing that the triangle corresponding to the given complex number is a 30-60-90 right triangle with short leg 5.)