SOLUTION: Find the square roots of the complex number. (Enter your answers as a comma-separated list.) 13i

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Question 1174537: Find the square roots of the complex number. (Enter your answers as a comma-separated list.)
13i

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


13i+=+13%2Acis%28pi%2F2%29

By deMoivre's Theorem, the primary square root is

sqrt%2813i%29+=+sqrt%2813%29%2Acis%28%28pi%2F2%29%2F2%29+=+sqrt%2813%29%2Acis%28pi%2F4%29

The n n-th roots of a complex number have the same magnitude, and they are separated in the complex plane by angles of (2pi)/n.

For this problem with square roots, the other square root is (2pi)/2 = pi radians past the primary square root: sqrt%2813%29%2Acis%285pi%2F4%29

ANSWERS:
sqrt%2813%29%2Acis%28pi%2F4%29
sqrt%2813%29%2Acis%285pi%2F4%29