Given that&nbsp;${z}$ and ${w}$ are complex numbers, prove that
${{{\left| z+w \right|}^{2}}-{{\left| z+w^{*}\right|}^{2}}=4 \, \mathrm{Im}\, z}$ ${\mathrm{Im}\, w}$,
where&nbsp;${w^*}$ denotes the complex conjugate of ${w}$.

Given that ${z}$ and ${w}$ are complex numbers, prove that

${{{\left| z+w \right|}^{2}}-{{\left| z+w^{*}\right|}^{2}}=4 \, \mathrm{Im}\, z}$ ${\mathrm{Im}\, w}$,

where ${w^*}$ denotes the complex conjugate of ${w}$.

Applying Complex Conjugate Identities

Complex Numbers

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Complex Numbers Q5

Complex Numbers Q5

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