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

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

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