Solve for N (complex solution)
\left\{\begin{matrix}N=\frac{2\pi n_{1}i}{\ln(x)}\text{, }n_{1}\in \mathrm{Z}\text{, }&x\neq 1\text{ and }x\neq 0\\N\in \mathrm{C}\text{, }&x=1\end{matrix}\right.
Solve for x (complex solution)
x=e^{-\frac{2\pi n_{1}\left(Im(N)+iRe(N)\right)}{\left(Re(N)\right)^{2}+\left(Im(N)\right)^{2}}}
n_{1}\in \mathrm{Z}
Solve for N
\left\{\begin{matrix}N=0\text{, }&x\neq 0\text{ and }|x|\neq 1\\N\in \mathrm{R}\text{, }&x=1\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x=-1\text{, }&Numerator(N)\text{bmod}2=0\text{ and }Denominator(N)\text{bmod}2=1\\x\neq 0\text{, }&N=0\end{matrix}\right.
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