Powers of Complex Numbers

DeMoivre's Theorem:

(x + yi)n = [r (cos q + i sin q )] n = r n[cos (nq ) + i sin (nq )]

Proof:

[r (cos q + i sin q )] [r (cos q + i sin q )] = r 2[cis (q + q )] = r 2[cis (2q )]

r 2[cis (2q )]  r cis q  =  r 3cis (3q)

etc.

Example:

[2 cis 72o)]5 = 32 cis 360o or 32

Problems

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