$z^n=\left(x^n-\left(\frac{n}{2}\right)x^{n-2}{y}^2+\left(\frac{n}{4}\right)x^{n-4}{y}^4-\cdots \right)+i\left(\left(\frac{n}{1}\right)x^{n-1}y-\left(\frac{n}{3}\right)x^{n-3}{y}^3+\cdots \right)$