SOLUTION: Find (sqrt3 + i) using DeMoivre's Theorem? Leave answer in a polar form. Show work!

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Question 280701: Find (sqrt3 + i) using DeMoivre's Theorem?
Leave answer in a polar form. Show work!
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
DeMoivre's Theorem is usually used to raise complex numbers to a power. So I suspect that you left out an exponent. If so and if you are still not able to figure out the problem after reading what follows, please repost your question.

(Note: For unknown reasons Algebra.com's formula software does not handle notation for inverse functions well. So I will use "acos" in place of cos^-1 and asin for sin^-1 in the expressions below.)
If all you have to do is rewrite the complex number in polar form then the formula is:

Using this on your complex number we get:

Simplifying:


2%28cos%28acos%28sqrt%283%29%2F2%29%29+%2B+i%2Asin%28asin%281%2F2%29%29%29
Using degrees, acos%28sqrt%283%29%2F2%29+=+asin%281%2F2%29+=+30. (Use pi%2F6 for radians.) We now have:
2%28cos%2830%29+%2B+i%2Asin%2830%29%29
With polar form and DeMoivre's Theorem, it is very easy to raise complex numbers to powers.