givn that z = 1−i(√3) express z in the form z = r(cosθ + isinθ), hence express z^7 in the form re^(iθ)


Question and Answers Forum

All Questions Topic List
Others Questions
Previous in All Question Next in All Question
Previous in Others Next in Others
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

	$t h a n k s s i r, i a p p r e c i a t e$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum