For any two complex number $z_{1}$ and $z_{2}$ and any real numbers a and b;
$| (a z_{1} - b z_{2}) |^{2}$ + $| (b z_{1} - a z_{2}) |^{2}$ =

(+)()

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Solution

The correct option is B
(+)

$| (a z_{1} - b z_{2}) |^{2}$ + $| (b z_{1} - a z_{2}) |^{2}$

= $a^{2}$ $| z_{1} |^{2}$ + $b^{2}$ $| z_{2} |^{2}$ -2Re(ab)| $z_{1}$ ${¯ ¯ ¯ z}_{2}$ |+ $b^{2}$ $| z_{1} |^{2}$ + $a^{2}$ $| z_{2} |^{2}$ +2Re(ab)| $z_{2}$ ${¯ ¯ ¯ z}_{1}$ |

= $(a^{2} + b^{2})$ $(| z_{1} |^{2} + (| z_{2} |^{2})$

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For any two complex number z1 and z2 and any real numbers a and b; |(az1−bz2)|2 + |(bz1−az2)|2 =

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