Complex Trigonometry

Algebra Level pending

If $$u+iv=\csc { \left( \frac { \pi }{ 4 } +ix \right) }$$, where $$i=\sqrt { -1 }$$, find the value of $$\frac { { ({ u }^{ 2 }+{ v }^{ 2 }) }^{ 2 } }{ ({ u }^{ 2 }-{ v }^{ 2 }) }$$.

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