A^c=B megoldása

$$A ^ { c } = B$$

Megoldás a(z) A változóra (complex solution)

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

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

Megoldás a(z) B változóra (complex solution)

$$B=A^{c}$$

Megoldás a(z) A változóra

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

Megoldás a(z) B változóra

$$B=A^{c}$$

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