Cunning Complex 4

Algebra Level 4

Let  z1 =10+6i\ { z }_{ 1 } \ =10+6i and  z2 =4+6i\ { z }_{ 2 } \ =4+6i. And suppose zz is any complex number such that the arguement of zz1zz2=π4\frac { z-{ z }_{ 1 } }{ z-{ z }_{ 2 } } =\frac { \pi }{ 4 }.

Find the value of z79i\left| z-7-9i \right| .

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