Solve for P (complex solution)
P=-2\sqrt{2}ie^{i\theta +\frac{\pi i}{4}}+2\sqrt{2}ie^{-i\theta -\frac{\pi i}{4}}
Solve for θ (complex solution)
\theta =-i\ln(\frac{i\sqrt{P^{2}-32}+iP}{8})+2\pi n_{1}-\frac{\ln(2)i}{2}-\frac{\pi }{4}\text{, }n_{1}\in \mathrm{Z}
\theta =-i\ln(-i\sqrt{P^{2}-32}+iP)+2\pi n_{2}+\frac{5i\ln(2)}{2}-\frac{\pi }{4}\text{, }n_{2}\in \mathrm{Z}
Solve for P
P=4\sqrt{2}\sin(\frac{4\theta +\pi }{4})
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