Solve i(x+y/z)^d=1

$$i ( \frac { x + y } { z } ) ^ { d } = 1$$

Solve for d

$$d=\frac{2\pi n_{1}i}{\ln(\frac{x+y}{z})}+\frac{3\pi i}{2\ln(\frac{x+y}{z})}$$

$$n_{1}\in \mathrm{Z}$$

$$x\neq z-y\text{ and }x\neq -y\text{ and }z\neq 0$$

Solve for x

$$x=-\left(y-ze^{-\frac{2i\pi n_{1}Re(d)}{\left(Re(d)\right)^{2}+\left(Im(d)\right)^{2}}-\frac{2\pi n_{1}Im(d)}{\left(Re(d)\right)^{2}+\left(Im(d)\right)^{2}}+\frac{\pi \left(3Im(d)+3iRe(d)\right)}{2\left(\left(Re(d)\right)^{2}+\left(Im(d)\right)^{2}\right)}}\right)$$

$$n_{1}\in \mathrm{Z}$$

$$z\neq 0\text{ and }\left(Re(d)\right)^{2}+\left(Im(d)\right)^{2}\neq 0$$