Solve z=w^(3y+2ix).text{where}w=x

$$z = w ^ { ( 3 y + 2 i x ) } . \text { where } w = x$$

Solve for w

$$w=e^{\frac{-2iIm(x)arg(z)+2Re(x)arg(z)+3Im(y)arg(z)+3iRe(y)arg(z)}{12Re(x)Im(y)-12Re(y)Im(x)+4\left(Re(x)\right)^{2}+4\left(Im(x)\right)^{2}+9\left(Re(y)\right)^{2}+9\left(Im(y)\right)^{2}}+\frac{4\pi n_{1}iIm(x)}{12Re(x)Im(y)-12Re(y)Im(x)+4\left(Re(x)\right)^{2}+4\left(Im(x)\right)^{2}+9\left(Re(y)\right)^{2}+9\left(Im(y)\right)^{2}}-\frac{6\pi n_{1}iRe(y)}{12Re(x)Im(y)-12Re(y)Im(x)+4\left(Re(x)\right)^{2}+4\left(Im(x)\right)^{2}+9\left(Re(y)\right)^{2}+9\left(Im(y)\right)^{2}}-\frac{4\pi n_{1}Re(x)}{12Re(x)Im(y)-12Re(y)Im(x)+4\left(Re(x)\right)^{2}+4\left(Im(x)\right)^{2}+9\left(Re(y)\right)^{2}+9\left(Im(y)\right)^{2}}-\frac{6\pi n_{1}Im(y)}{12Re(x)Im(y)-12Re(y)Im(x)+4\left(Re(x)\right)^{2}+4\left(Im(x)\right)^{2}+9\left(Re(y)\right)^{2}+9\left(Im(y)\right)^{2}}}\left(|z|\right)^{\frac{-2iRe(x)-3iIm(y)+3Re(y)-2Im(x)}{12Re(x)Im(y)-12Re(y)Im(x)+4\left(Re(x)\right)^{2}+4\left(Im(x)\right)^{2}+9\left(Re(y)\right)^{2}+9\left(Im(y)\right)^{2}}}$$

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

Solve for x

$$\left\{\begin{matrix}x=\frac{\pi n_{1}}{\ln(w)}-\frac{i\log_{w}\left(z\right)}{2}+\frac{3iy}{2}\text{, }n_{1}\in \mathrm{Z}\text{, }&w\neq 1\text{ and }w\neq 0\text{ and }z\neq 0\\x\in \mathrm{C}\text{, }&\left(w=1\text{ and }z=1\right)\text{ or }\left(w=0\text{ and }z=0\right)\end{matrix}\right.$$