if Z=cosθ+isinθ prove that Z^5 −(1/Z^2 )=2isin5θ help me sir


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Question Number 127558 by mohammad17 last updated on 30/Dec/20

$i f Z = c o s θ + i s i n θ p r o v e t h a t$ $Z^{5} - \frac{1}{Z^{2}} = 2 i s i n 5 θ$ $h e l p m e s i r$
Commented by mohammad17 last updated on 30/Dec/20

$?$
Commented by MJS_new last updated on 31/Dec/20

$z^{5} + \frac{1}{z^{2}} = \cos 5 θ - \cos 2 θ + i (\sin 5 θ + \sin 2 θ)$
	Answered by mohammad17 last updated on 30/Dec/20

	$h o w c a n s o l v e t h i s$
	Answered by Dwaipayan Shikari last updated on 30/Dec/20

	$z^{5} - z^{- 5} = e^{5 i θ} - e^{- 5 i θ} = 2 i s i n 5 θ$
	Commented by mohammad17 last updated on 30/Dec/20

	$p u t s i r h o w b e c a m e z^{- 5} c a n y o u g i v e m e s t e b s$
	Commented by Dwaipayan Shikari last updated on 30/Dec/20

	$I t h i n k m i s t a k e i n q u e s t i o n . I t s h o u l d b e z^{- 5} i n s t e a d o f z^{- 2}$
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