Solve for a
a=1+3i-ib
Solve for b
b=ia+\left(3-i\right)
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1+3i=a+bi
Multiply 1+i and 2+i to get 1+3i.
a+bi=1+3i
Swap sides so that all variable terms are on the left hand side.
a=1+3i-bi
Subtract bi from both sides.
a=1+3i-ib
Multiply -1 and i to get -i.
1+3i=a+bi
Multiply 1+i and 2+i to get 1+3i.
a+bi=1+3i
Swap sides so that all variable terms are on the left hand side.
bi=1+3i-a
Subtract a from both sides.
ib=1+3i-a
The equation is in standard form.
\frac{ib}{i}=\frac{1+3i-a}{i}
Divide both sides by i.
b=\frac{1+3i-a}{i}
Dividing by i undoes the multiplication by i.
b=ia+\left(3-i\right)
Divide 1+3i-a by i.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}