Solve for a
a=ib+\left(-1-2i\right)
Solve for b
b=2-i-ia
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5-2i-a+bi=6
Calculate the square root of -4 and get 2i.
-2i-a+bi=6-5
Subtract 5 from both sides.
-2i-a+bi=1
Subtract 5 from 6 to get 1.
-a+bi=1+2i
Add 2i to both sides.
-a=1+2i-bi
Subtract bi from both sides.
-a=1+2i-ib
Multiply -1 and i to get -i.
\frac{-a}{-1}=\frac{1+2i-ib}{-1}
Divide both sides by -1.
a=\frac{1+2i-ib}{-1}
Dividing by -1 undoes the multiplication by -1.
a=ib+\left(-1-2i\right)
Divide 1+2i-ib by -1.
5-2i-a+bi=6
Calculate the square root of -4 and get 2i.
-2i-a+bi=6-5
Subtract 5 from both sides.
-2i-a+bi=1
Subtract 5 from 6 to get 1.
-a+bi=1+2i
Add 2i to both sides.
bi=1+2i+a
Add a to both sides.
ib=a+\left(1+2i\right)
The equation is in standard form.
\frac{ib}{i}=\frac{a+\left(1+2i\right)}{i}
Divide both sides by i.
b=\frac{a+\left(1+2i\right)}{i}
Dividing by i undoes the multiplication by i.
b=2-i-ia
Divide 1+2i+a by 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}