Solve for z
z=1-i
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1+i=zi^{5}
Variable z cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by z.
1+i=zi
Calculate i to the power of 5 and get i.
zi=1+i
Swap sides so that all variable terms are on the left hand side.
z=\frac{1+i}{i}
Divide both sides by i.
z=\frac{-1+i}{-1}
Multiply both numerator and denominator of \frac{1+i}{i} by imaginary unit i.
z=1-i
Divide -1+i by -1 to get 1-i.
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}