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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