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Ooh too Complex

Let z1=6+iz_1 = 6+i and z2=43iz_2 = 4-3i.
Let zz be a complex number such that arg(zz1z2z)=π2\text{arg}\left(\dfrac{z-z_1}{z_2-z}\right)=\dfrac{\pi}{2}, and z(5i)|z-(5-i)|=m\sqrt{m}.

Find m.m.

Details and Assumptions:

  • arg(x) \text{arg}(x) is the argument of xx.
  • z1,z2,z_1,z_2, and zz are complex numbers.

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