Solve for p (complex solution)
p=ie^{-iϕ-\frac{\pi i}{4}}-ie^{iϕ+\frac{\pi i}{4}}
Solve for ϕ (complex solution)
ϕ=-i\ln(\frac{i\sqrt{p^{2}-4}+ip}{2})+2\pi n_{1}-\frac{\pi }{4}\text{, }n_{1}\in \mathrm{Z}
ϕ=-i\ln(\frac{-i\sqrt{p^{2}-4}+ip}{2})+2\pi n_{2}-\frac{\pi }{4}\text{, }n_{2}\in \mathrm{Z}
Solve for p
p=2\sin(\frac{4ϕ+\pi }{4})
Solve for ϕ
ϕ=\frac{4\arcsin(\frac{p}{2})+8\pi n_{1}-\pi }{4}\text{, }n_{1}\in \mathrm{Z}
ϕ=\frac{-4\arcsin(\frac{p}{2})+8\pi n_{2}+3\pi }{4}\text{, }n_{2}\in \mathrm{Z}\text{, }|p|\leq 2
Share
Copied to clipboard
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}