Solve for P
\left\{\begin{matrix}P=\frac{z-iIm(z)}{ez}\text{, }&z\neq 0\\P\in \mathrm{C}\text{, }&z=0\end{matrix}\right.
Quiz
Complex Number
5 problems similar to:
z = \operatorname { Pe } ( z ) + i \operatorname { Im } ( z )
Share
Copied to clipboard
Pez+iIm(z)=z
Swap sides so that all variable terms are on the left hand side.
Pez=z-iIm(z)
Subtract iIm(z) from both sides.
ePz=-iIm(z)+z
Reorder the terms.
ezP=z-iIm(z)
The equation is in standard form.
\frac{ezP}{ez}=\frac{z-iIm(z)}{ez}
Divide both sides by ez.
P=\frac{z-iIm(z)}{ez}
Dividing by ez undoes the multiplication by ez.
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}