Ooh too Complex

Algebra Level 3

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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