Solve for a
a=-\frac{ib}{2}+\left(-1+\frac{5}{2}i\right)
Solve for b
b=2ia+\left(5+2i\right)
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2a+bi=5i-2
Calculate the square root of -25 and get 5i.
2a=5i-2-bi
Subtract bi from both sides.
2a=5i-2-ib
Multiply -1 and i to get -i.
2a=-2+5i-ib
The equation is in standard form.
\frac{2a}{2}=\frac{-2+5i-ib}{2}
Divide both sides by 2.
a=\frac{-2+5i-ib}{2}
Dividing by 2 undoes the multiplication by 2.
a=-\frac{ib}{2}+\left(-1+\frac{5}{2}i\right)
Divide -2+5i-ib by 2.
2a+bi=5i-2
Calculate the square root of -25 and get 5i.
bi=5i-2-2a
Subtract 2a from both sides.
ib=-2+5i-2a
The equation is in standard form.
\frac{ib}{i}=\frac{-2+5i-2a}{i}
Divide both sides by i.
b=\frac{-2+5i-2a}{i}
Dividing by i undoes the multiplication by i.
b=2ia+\left(5+2i\right)
Divide -2+5i-2a by i.
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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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}