Precalculus - Powers and Roots of Complex Numbers

Step-by-step tutorial.
Determine the power of a complex number using De Moivre's Theorem.
Determine the root of a complex number using n-th root formula.

De Moivre’s Theorem: [r(cos⁡θ+i sin⁡θ)]^n=r^n (cos ⁡nθ+i sin ⁡nθ)

The nth root of a complex number:
[r(cos⁡θ+i sin⁡θ)]^(1/n)=r^(1/n) [cos (θ+2kπ)/n+i sin⁡ (θ+2kπ)/n], where k=0,1,2,…,n-1.