if ∣z_1 ∣=∣z_2 ∣=∣z_3 ∣=1 and ∣(1/z_1 )∣+∣(1/z_2 )∣+∣(1/z_3 )∣=1 find ∣z_1 +z_2 +z_3 ∣=? z_1 ,z_2 ,z


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Question Number 130818 by Study last updated on 29/Jan/21

$i f ∣ z_{1} ∣=∣ z_{2} ∣=∣ z_{3} ∣= 1$ $a n d ∣ \frac{1}{z_{1}} ∣ + ∣ \frac{1}{z_{2}} ∣ + ∣ \frac{1}{z_{3}} ∣= 1$ $f i n d ∣ z_{1} + z_{2} + z_{3} ∣= ?$ $z_{1}, z_{2}, z_{3} \in c o m p l e x n u m b e r$
	Answered by TheSupreme last updated on 29/Jan/21

	$z_{i} = ρ_{i} e^{i θ_{i}}$ $ρ_{1} = ρ_{2} = ρ_{3} = 1$ $\frac{1}{ρ_{1}} + \frac{1}{ρ_{2}} + \frac{1}{ρ_{3}} = 1$ $3 = 1$ $i m p o s s i b l e$ $w e c a n e v a l u a t e$ $\frac{1}{z_{1}} + \frac{1}{z_{2}} + \frac{1}{z_{3}} = 1$ $e^{- i θ_{1}} + e^{- i θ_{2}} + e^{- i θ_{3}} = 1$ $t h e n$ $e^{i θ_{1}} + e^{i θ_{2}} + e^{i θ_{3}} = {(e^{i θ_{1}} + e^{i θ_{2}} + e^{i θ_{3}})}^{} = 1^{} = 1$
	Commented by Study last updated on 30/Jan/21

	$t h a n k s s i r$
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