z n = ( x n - ( n 2 ) x n - 2 y 2 + ( n 4 ) x n - 4 y 4 - ⋯ ) + i ( ( n 1 ) x n - 1 y - ( n 3 ) x n - 3 y 3 + ⋯ ) 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)