Too Complex!

Algebra Level 4

Consider the complex numbers \(z_1 = 10+6i, z_2 = 4 + 6i \) such that there exist a complex number \(z\) that satisfy the condition \( \displaystyle \text{arg} \left( \frac{z-z_1}{z-z_2} \right) = \frac \pi4\). Find the value of \(|z-7-9i| \).

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