DeMoivre's Theorem - Concept

Concept Concept (1)

We know how to multiply complex numbers, but raising complex numbers to a high integer power would involve a lot of computation. Fortunately we have DeMoivre's Theorem, which gives us a more simple solution to raising complex numbers to a power. DeMoivre's Theorem can also be used to calculate the roots of complex numbers. DeMoivre's Theorem uses the trigonometric form of complex numbers.

Sample Sample Problems (2)

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DeMoivre's Theorem - Problem 1
Problem 1
How to simplify integer powers of a complex number, z = 1/2 + (root(3)/2)*i, by converting to trigonometric form.
DeMoivre's Theorem - Problem 2
Problem 2
How to compute several integer powers of a complex number, z = 1 + i, by converting to trigonometric form.