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If $z_{1} a n d z_{2}$ are any two complex numbers then $| z_{1} + z_{2} |^{2} + | z_{1} - z_{2} |^{2}$ is equal to

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$2 | z_{1} |^{2} + 2 | z_{2} |^{2}$

$2 | z_{1} | | z_{2} |$

$2 | z_{1} |^{2} | z_{2} |^{2}$

$| z_{1} |^{2} + | z_{2} |^{2}$

answer is B.

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Detailed Solution

$| z_{1} + z_{2} |^{2} + | z_{1} - z_{2} |^{2}$

$= {(x_{1} + x_{2})}^{2} + {(y_{1} + y_{2})}^{2} + {(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}$

$= 2 (x_{1}^{2}) + 2 (y_{1}^{2}) + 2 (x_{2}^{2}) + 2 (y_{2}^{2}) = 2 | z_{1} |^{2} + 2 | z_{2} |^{2}$

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