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

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