z = 1− i(√3) express z in the form r(cosθ +isinθ) also express z^7 in the form re^(iθ) .


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Question Number 65168 by Rio Michael last updated on 25/Jul/19

$z = 1 - i \sqrt{3}$ $e x p r e s s z i n t h e f o r m r (c o s θ + i s i n θ) a l s o e x p r e s s z^{7} i n t h e f o r m$ ${r e}^{i θ} .$
	Answered by mr W last updated on 25/Jul/19

	$z = 1 - i \sqrt{3}$ $= 2 (\frac{1}{2} - i \frac{\sqrt{3}}{2})$ $= 2 (\cos \frac{5 π}{3} + i \sin \frac{5 π}{3})$ $= 2 e^{i \frac{5 π}{3}}$
	Answered by meme last updated on 25/Jul/19
	$z=2(((1−i(√3))/2))=2{cos(−(Π/3))+isin(−(Π/3))} z^7 =2^7 (cos(−((7Π)/3))+isin(−((7Π)/3))$
	$z = 2 (\frac{1 - i \sqrt{3}}{2}) = 2 {c o s (- \frac{Π}{3}) + i s i n (- \frac{Π}{3})}$ $z^{7} = 2^{7} (c o s (- \frac{7 Π}{3}) + i s i n (- \frac{7 Π}{3})$
	Commented by meme last updated on 25/Jul/19

	$z^{7} = 128 e^{i \frac{7 Π}{3}}$
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