Solve (a + 2i)(b - i) = i | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(a+2i)(b-i)=i$$

Solve for a

$a=-\frac{2ib+\left(2-i\right)}{b-i}$
$b\neq i$

Steps for Solving Linear Equation

Use the distributive property to multiply $a+2i$ by $b-i$.

$$ab-ia+2ib+2=i$$

Subtract $2ib$ from both sides.

$$ab-ia+2=i-2ib$$

Subtract $2$ from both sides.

$$ab-ia=i-2ib-2$$

Combine all terms containing $a$.

$$\left(b-i\right)a=i-2ib-2$$

The equation is in standard form.

$$\left(b-i\right)a=-2+i-2ib$$

Divide both sides by $b-i$.

$$\frac{\left(b-i\right)a}{b-i}=\frac{-2+i-2ib}{b-i}$$

Dividing by $b-i$ undoes the multiplication by $b-i$.

$$a=\frac{-2+i-2ib}{b-i}$$

Solve for b

$b=-\frac{2-i-ia}{a+2i}$
$a\neq -2i$

Steps for Solving Linear Equation

Use the distributive property to multiply $a+2i$ by $b-i$.

$$ab-ia+2ib+2=i$$

Subtract $-ia$ from both sides.

$$ab+2ib+2=i-\left(-ia\right)$$

Subtract $2$ from both sides.

$$ab+2ib=i-\left(-ia\right)-2$$

Multiply $-1$ and $-i$ to get $i$.

$$ab+2ib=i+ia-2$$

Combine all terms containing $b$.

$$\left(a+2i\right)b=i+ia-2$$

The equation is in standard form.

$$\left(a+2i\right)b=ia+\left(-2+i\right)$$

Divide both sides by $a+2i$.

$$\frac{\left(a+2i\right)b}{a+2i}=\frac{ia+\left(-2+i\right)}{a+2i}$$

Dividing by $a+2i$ undoes the multiplication by $a+2i$.

$$b=\frac{ia+\left(-2+i\right)}{a+2i}$$