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Question Number 75178 by Rio Michael last updated on 08/Dec/19

g i v n t h a t z = 1 - i \sqrt{3} e x p r e s s z i n t h e f o r m

z = r (c o s θ + i s i n θ), h e n c e e x p r e s s

z^{7} i n t h e f o r m {r e}^{i θ}

Answered by mr W last updated on 08/Dec/19

z = 1 - \sqrt{3} i = 2 (\frac{1}{2} - \frac{\sqrt{3}}{2} i) = 2 (\cos \frac{5 π}{3} + i \sin \frac{5 π}{3})

= 2 e^{\frac{5 π i}{3}}

z^{7} = 2^{7} e^{\frac{35 π i}{3}} = 128 e^{\frac{5 π i}{3}}

Commented by Rio Michael last updated on 08/Dec/19

t h a n k s s i r, i a p p r e c i a t e