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Question Number 164473 by mathocean1 last updated on 17/Jan/22

S h o w f o r z_{1}; z_{2} \in C t h a t :

∣ z_{1} + z_{2} ∣^{2} + ∣ z_{1} - z_{2} ∣^{2} = 2 (∣ z_{1} ∣^{2} + ∣ z_{2} ∣^{2}) .

Answered by puissant last updated on 19/Jan/22

∣ z_{1} + z_{2} ∣^{2} + ∣ z_{1} - z_{2} ∣^{2} = ∣ z_{1} ∣^{2} + 2 ∣ z_{1} ∣∣ z_{2} ∣ + ∣ z_{2} ∣^{2} + ∣ z_{1} ∣^{2} - 2 ∣ z_{1} ∣∣ z_{2} ∣ + ∣ z_{2} ∣^{2}

= 2 (∣ z_{1} ∣^{2} + ∣ z_{2} ∣^{2})

Commented by mathocean1 last updated on 19/Jan/22

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