# Ooh too Complex

Algebra Level 2

Let $$z_1 = 6+i$$ and $$z_2 = 4-3i$$.
Let $$z$$ be a complex number such that $$\text{arg}\left(\dfrac{z-z_1}{z_2-z}\right)=\dfrac{\pi}{2}$$, and $$|z-(5-i)|$$=$$\sqrt{m}$$.

Find $$m.$$


Details and Assumptions:

• $$\text{arg}(x)$$ is the argument of $$x$$.
• $$z_1,z_2,$$ and $$z$$ are complex numbers.
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