Solve for a
a=\frac{5-ib}{2}
Solve for b
b=2ia-5i
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2a+i=4-bi+i+1
Add 1 to both sides.
2a=4-bi+i+1-i
Subtract i from both sides.
2a=4-bi+1
Do the additions in i+1-i.
2a=4-ib+1
Multiply -1 and i to get -i.
2a=5-ib
Add 4 and 1 to get 5.
\frac{2a}{2}=\frac{5-ib}{2}
Divide both sides by 2.
a=\frac{5-ib}{2}
Dividing by 2 undoes the multiplication by 2.
4-bi+i=2a-1+i
Swap sides so that all variable terms are on the left hand side.
4-bi=2a-1+i-i
Subtract i from both sides.
4-bi=2a-1
Do the additions in -1+i-i.
4-ib=2a-1
Multiply -1 and i to get -i.
-ib=2a-1-4
Subtract 4 from both sides.
-ib=2a-5
Subtract 4 from -1 to get -5.
\frac{-ib}{-i}=\frac{2a-5}{-i}
Divide both sides by -i.
b=\frac{2a-5}{-i}
Dividing by -i undoes the multiplication by -i.
b=2ia-5i
Divide 2a-5 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}