z-1-i-3-express-z-in-the-form-r-cos-isin-also-express-z-7-in-the-form-re-i-

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 (\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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