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