Complex number 4

Algebra Level 3

\[\large\begin{cases} {56x +33y = -\frac y{x^2+y^2} } \\ {33x -56y = \frac x{x^2+y^2} } \end{cases} \]

Given that \(x,y\) are complex numbers that satisfy the system of equations above and that \( |x| + |y| \) equals \(\frac pq\) for coprime positive integers \(p,q\), evaluate \(6p-q\).

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