M=V^t lösen

$$M = V ^ { t }$$

Nach V auflösen (komplexe Lösung)

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

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

Nach M auflösen

$$M=V^{t}$$

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

Nach V auflösen

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