Solve it like a Mathematician.

Algebra Level 5

Let z1=10+6iz_1=10+6i and z2=4+6iz_2=4+6i. If zz be a complex number such that arg(zz1zz2)=π4\text{arg}\left( \frac{z-z_1}{z-z_2} \right)=\frac{\pi}{4}, then find the value of z79i|z-7-9i|. Give your answer up to 3 decimal places.

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