Solve y=-4x^rix

$$y = - 4 x ^ { r } i x$$

Solve for r

$$\left\{\begin{matrix}r=\frac{2\pi n_{1}i}{\ln(x)}+\log_{x}\left(\frac{iy}{4}\right)-1\text{, }n_{1}\in \mathrm{Z}\text{, }&x\neq 1\text{ and }x\neq 0\text{ and }y\neq 0\\r\in \mathrm{C}\text{, }&\left(x=0\text{ and }y=0\right)\text{ or }\left(x=1\text{ and }y=-4i\right)\end{matrix}\right.$$

Solve for x

$$x=4^{\frac{-Re(r)-1+iIm(r)}{\left(Re(r)\right)^{2}+\left(Im(r)\right)^{2}+2Re(r)+1}}\left(|y|\right)^{\frac{Re(r)\left(Im(r)\right)^{2}-iIm(r)\left(Re(r)\right)^{2}+\left(Re(r)\right)^{3}-i\left(Im(r)\right)^{3}-2iRe(r)Im(r)+3\left(Re(r)\right)^{2}+\left(Im(r)\right)^{2}+3Re(r)-iIm(r)+1}{\left(\left(Re(r)\right)^{2}+\left(Im(r)\right)^{2}+2Re(r)+1\right)^{2}}}e^{\frac{Im(r)arg(\frac{iy}{4})+iRe(r)arg(\frac{iy}{4})+iarg(\frac{iy}{4})}{\left(Re(r)\right)^{2}+\left(Im(r)\right)^{2}+2Re(r)+1}-\frac{2\pi n_{1}iRe(r)}{\left(Re(r)\right)^{2}+\left(Im(r)\right)^{2}+2Re(r)+1}-\frac{2\pi n_{1}Im(r)}{\left(Re(r)\right)^{2}+\left(Im(r)\right)^{2}+2Re(r)+1}-\frac{2\pi n_{1}i}{\left(Re(r)\right)^{2}+\left(Im(r)\right)^{2}+2Re(r)+1}}$$

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