For any two complex numbers and

MATHEMATICS · Subjective · AoPS · Mathematics · Complex Numbers · Complex Numbers

Problem

2. For any two complex numbers

z_{1}

and

z_{2}

, prove that

\operatorname{Re}\left(z_{1} z_{2}\right)=\operatorname{Re} z_{1} \operatorname{Re} z_{2}-\operatorname{Im} z_{1} \operatorname{Im} z_{2}

.

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