If $| z_{1} | = 1, | z_{2} | = 2$ , then 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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N o n e o f t h e s e

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Solution

The correct option is D $N o n e o f t h e s e$
Given:- $| z_{1} | = 1, | z_{2} | = 2$
Therefore,
${| z_{1} + z_{2} |}^{2} + {| z_{1} - z_{2} |}^{2}$
$= {| z_{1} |}^{2} + {| z_{2} |}^{2} + 2 z_{1} z_{2} + {| z_{1} |}^{2} + {| z_{2} |}^{2} - 2 z_{1} z_{2}$
$= 2 ({| z_{1} |}^{2} + {| z_{2} |}^{2})$
$= 2 (1^{2} + 2^{2})$
$= 2 (1 + 4)$
$= 2 \times 5 = 10$

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If arg ( $Z_{1}$ ) = $α$ , arg ( $Z_{2}$ ) = $β$ , the value of $| Z_{1} + Z_{2} |^{2}$ is

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| arg (z_{1}) - arg (z_{2}) |

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