SOLUTION: Let z = -2 - 2i. Use DeMoivre’s Theorem to find z6.
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Question 1138390: Let z = -2 - 2i. Use DeMoivre’s Theorem to find z6.
Found 2 solutions by greenestamps, Alan3354:
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
|z| =
theta = 225 degrees = 5pi/4
According to deMoivre's Theorem,
|z^6| =
theta = 6*5pi/4 = 30pi/4 = 15pi/2 = 3pi/2
So
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Let z = -2 - 2i. Use DeMoivre’s Theorem to find z6.
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z = -2 - 2i.
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z = sqrt(2^2 + 2^2)cis(225) = 2sqrt(2)cis(225)
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z^6 = 64*8cis(1350)
z^6 = 512cis(270)
z^6 = 512(cos(270) + isin(270))
z^6 = -512i
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