# Too Complex!

Algebra Level 5

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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