For any two complex numbers \( z_{1}, z_{2} \) and any two real num...

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For any two complex numbers \( z_{1}, z_{2} \) and any two real numbers \( a, b \) show that
\( \mathrm{P} \) \( \left|a z_{1}-b z_{1}\right|^{2}+\left|b z_{1}+a z_{2}\right|^{2}=\left(a^{2}+b^{2}\right)\left(\left|z_{1}\right|^{2}+\left|z_{2}\right|^{2}\right) \)

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