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