find z_1 ,z_2 ∈C (1/(z_1 +z_2 ))=(1/z_1 )+(1/z


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Question Number 56192 by 121194 last updated on 11/Mar/19

$find z_{1}, z_{2} \in C$ $\frac{1}{z_{1} + z_{2}} = \frac{1}{z_{1}} + \frac{1}{z_{2}}$
	Answered by MJS last updated on 11/Mar/19
	$⇒ z_1 ^2 +z_1 z_2 +z_2 ^2 =0 ⇒ z_2 =z_1 (−(1/2)±((√3)/2)i) ∀z_1 ,z_2 ∈C\{0}$
	$\Rightarrow z_{1}^{2} + z_{1} z_{2} + z_{2}^{2} = 0$ $\Rightarrow z_{2} = z_{1} (- \frac{1}{2} \pm \frac{\sqrt{3}}{2} i) \forall z_{1}, z_{2} \in C ∖ {0}$
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