For any two complex numbers {z_1}and{z_2} and | vedclass

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Question

(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} - 2{\mathop{m Re}
olimits} (ab)|{z_1}{\overline z _

Vedclass · Accepted Answer

$({a^2} + {b^2})(|{z_1}{|^2} + |{z_2}{|^2})$

Vedclass · Answer

(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} - 2{\mathop{m Re}
olimits} (ab)|{z_1}{\overline z _2}|+ {b^2}|{z_1}{|^2} + $${a^2}|{z_2}{|^2} + 2{\mathop{m Re}
olimits} (ab)|{\overline z _1}{z_2}|$
$ = ({a^2} + {b^2})(|{z_1}{|^2} + |{z_2}{|^2})$

For any two complex numbers ${z_1}$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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