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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