Solve E=M^c

$$E = M ^ { c }$$

Solve for M (complex solution)

$$M=e^{\frac{Im(c)arg(E)+iRe(c)arg(E)}{\left(Re(c)\right)^{2}+\left(Im(c)\right)^{2}}-\frac{2\pi n_{1}iRe(c)}{\left(Re(c)\right)^{2}+\left(Im(c)\right)^{2}}-\frac{2\pi n_{1}Im(c)}{\left(Re(c)\right)^{2}+\left(Im(c)\right)^{2}}}\left(|E|\right)^{\frac{Re(c)-iIm(c)}{\left(Re(c)\right)^{2}+\left(Im(c)\right)^{2}}}$$

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

Solve for E

$$E=M^{c}$$

$$\left(M<0\text{ and }Denominator(c)\text{bmod}2=1\right)\text{ or }\left(M=0\text{ and }c>0\right)\text{ or }M>0$$

Solve for M

$$\left\{\begin{matrix}M=E^{\frac{1}{c}}\text{, }&\left(Numerator(c)\text{bmod}2=1\text{ and }Denominator(c)\text{bmod}2=1\text{ and }E<0\text{ and }E^{\frac{1}{c}}\neq 0\right)\text{ or }\left(E=0\text{ and }c>0\right)\text{ or }\left(E>0\text{ and }c\neq 0\right)\\M=-E^{\frac{1}{c}}\text{, }&\left(E<0\text{ and }Numerator(c)\text{bmod}2=1\text{ and }Numerator(c)\text{bmod}2=0\text{ and }Denominator(c)\text{bmod}2=1\text{ and }E^{\frac{1}{c}}\neq 0\right)\text{ or }\left(c\neq 0\text{ and }E>0\text{ and }Numerator(c)\text{bmod}2=0\text{ and }Denominator(c)\text{bmod}2=1\right)\text{ or }\left(Numerator(c)\text{bmod}2=0\text{ and }E=0\text{ and }c>0\right)\text{ or }\left(E>0\text{ and }c\neq 0\text{ and }E^{\frac{1}{c}}<0\text{ and }Numerator(c)\text{bmod}2=0\right)\\M\neq 0\text{, }&c=0\text{ and }E=1\end{matrix}\right.$$