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

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

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

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

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None of these

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Solution

The correct option is B
( $a^{2}$ + $b^{2}$ ) $(| z_{1} |^{2} + | z_{2} |^{2})$

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

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

The correct option is B (a2+b2) (|z1|2+|z2|2) |(az1−bz2)|2 + |(bz1−az2)|2 =a2|z1|2+b2|z2|2-2Re(ab)|z1¯¯¯z2|+b2|z1|2+a2|z2|2+2Re(ab)|z2¯¯¯z1| = (a2+b2)(|z1|2+(|z2|2)

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