If $| z_{1} | == 1, | z_{2} | = 2,$ , then the value of ${| z_{1} + z_{2} |}^{2} + {| z_{1} - z_{2} |}^{2}$ is equal to

2

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3

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4

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none of these

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Solution

The correct option is D none of these
$| z_{1} + z_{2} |^{2} + | z_{1} - z_{2} |^{2} = (z_{1} + z_{2}) (_{1} +_{2}) + (z_{1} - z_{2}) (_{1} -_{2})$

$\Rightarrow 2 z_{1}_{1} + 2 z_{2}_{2} = 2 (| z_{1} |^{2} + | z_{2} |^{2}) = 2 (1 + 4) = 10$

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