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Question Number 66421 by Rio Michael last updated on 14/Aug/19

s h o w t h a t f o r a g i v e n c o m p l e x n u m b e r z

z^{n} = r^{n} (c o s n θ + i s i n n θ)

Answered by MJS last updated on 14/Aug/19

z = r (\cos θ + i \sin θ) = r e^{i θ}

z^{n} = {(r e^{i θ})}^{n} = r^{n} e^{i n θ} = r^{n} (\cos n θ + i \sin n θ)

Commented by Rio Michael last updated on 15/Aug/19

t h a n k s s i r