Solve for θ (complex solution)
\theta =\left(-1\right)\left(\left(-i\right)\ln(r+\left(-1\right)\left(r^{2}-1\right)^{\frac{1}{2}})+2\pi n_{1}\right)^{\frac{1}{2}}\text{, }n_{1}\in \mathrm{Z}
\theta =\left(\left(-i\right)\ln(r+\left(-1\right)\left(r^{2}-1\right)^{\frac{1}{2}})+2\pi n_{1}\right)^{\frac{1}{2}}\text{, }n_{1}\in \mathrm{Z}
\theta =\left(-1\right)\left(\left(-i\right)\ln(r+\left(r^{2}-1\right)^{\frac{1}{2}})+2\pi n_{5}\right)^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}
\theta =\left(\left(-i\right)\ln(r+\left(r^{2}-1\right)^{\frac{1}{2}})+2\pi n_{5}\right)^{\frac{1}{2}}\text{, }n_{5}\in \mathrm{Z}
Solve for r
r=\cos(\theta ^{2})
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