If z^3 =z^� prove then ∣z∣=1.


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Question Number 32002 by rahul 19 last updated on 18/Mar/18

$I f z^{3} = \bar{z} p r o v e$ $t h e n ∣ z ∣= 1 .$
	Answered by Tinkutara last updated on 18/Mar/18

	$z^{3} = \bar{z}$ $∣ z^{3} ∣=∣ \bar{z} ∣$ $∣ z ∣^{3} =∣ z ∣$ $∣ z ∣^{2} = 1$ $∣ z ∣= 1$
	Commented by Tinkutara last updated on 18/Mar/18

	$∣ z ∣ i s a l w a y s ⩾ 0 .$ $I f z = x + i y$ $t h e n ∣ z ∣= \sqrt{x^{2} + y^{2}}, w h e r e b o t h x, y \in R$ $a n d s q u a r e r o o t o f r e a l n u m b e r i s$ $t a k e n a s r e a l n u m b e r o n l y .$
	Commented by rahul 19 last updated on 18/Mar/18

	$t h a n k u!$
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