Complexity! (1)

Algebra Level 3

\[\begin{cases} \ \ \ z=x-iy \\ \sqrt[3]z=p+iq \end{cases}\]

Complex number \(z\) satisfies the system of equations above. Find the value of \(\dfrac{\left( \frac{x}{p} + \frac{y}{q} \right) }{p^2 + q^2}\).

Notation: \(i = \sqrt{-1}\) denotes the imaginary unit.


For more problems on complex numbers, click here.

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