Solve for z
z=3+i
Assign z
z≔3+i
Share
Copied to clipboard
z=1\times 2+1\left(-i\right)+2i-i^{2}
Multiply complex numbers 1+i and 2-i like you multiply binomials.
z=1\times 2+1\left(-i\right)+2i-\left(-1\right)
By definition, i^{2} is -1.
z=2-i+2i+1
Do the multiplications in 1\times 2+1\left(-i\right)+2i-\left(-1\right).
z=2+1+\left(-1+2\right)i
Combine the real and imaginary parts in 2-i+2i+1.
z=3+i
Do the additions in 2+1+\left(-1+2\right)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}