Let \( z_{1}=10+6 i \) and \( z_{2}=4+6 i \). If \( z \) is any complex number such that the arg...

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Let \( z_{1}=10+6 i \) and \( z_{2}=4+6 i \). If \( z \) is any complex number such that the argument of \( \left(z-z_{1}\right) /\left(z-z_{2}\right) \) is
P \( \pi / 4 \), then prove that \( |z-7-9 i|=3 \sqrt{2} \). \( \quad(1991,4 \mathrm{M}) \)

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