SOLUTION: Let z = -2 - 2i. Use DeMoivre’s Theorem to find z6.

Algebra ->  Trigonometry-basics -> SOLUTION: Let z = -2 - 2i. Use DeMoivre’s Theorem to find z6.      Log On


   

Question 1138390: Let z = -2 - 2i. Use DeMoivre’s Theorem to find z6.
Found 2 solutions by greenestamps, Alan3354:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


|z| = sqrt%282%5E2%2B2%5E2%29+=+sqrt%288%29+=+2%2Asqrt%282%29

theta = 225 degrees = 5pi/4

According to deMoivre's Theorem,

|z^6| = %282%2Asqrt%282%29%29%5E6+=+512
theta = 6*5pi/4 = 30pi/4 = 15pi/2 = 3pi/2

So z%5E6+=+-512i

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Let z = -2 - 2i. Use DeMoivre’s Theorem to find z6.
---------
z = -2 - 2i.
---
z = sqrt(2^2 + 2^2)cis(225) = 2sqrt(2)cis(225)
---
z^6 = 64*8cis(1350)
z^6 = 512cis(270)
z^6 = 512(cos(270) + isin(270))
z^6 = -512i