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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