# Isnt it Max or min?

Algebra Level 4

If $$z_{1}=10+6i$$ and $$z_{2}=4+6i$$ are two complex numbers such that

$\large \arg \left(\dfrac{z-z_{1}}{z-z_{2}}\right)=\dfrac{\pi}{4}$

Then $$|z-7-9i| = a\sqrt{b}$$, where $$a$$ and $$b$$ are positive integers with $$b$$ being square free. Input $$2(a+b)$$.

Notations:

• $$\arg(\cdot)$$ denotes argument or amplitude of a complex number.
• $$| \cdot |$$ denotes as modulus of a complex number.

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