Solve (2 + 3i)(a - bi) = 0 | 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

$$(2+3i)(a-bi)=0$$

Solve for a

$a=ib$

Solution Steps

Divide both sides by $2+3i$. Zero divided by any non-zero number gives zero.

$$a-bi=0$$

Add $bi$ to both sides.

$$a=0+bi$$

Anything plus zero gives itself.

$$a=bi$$

Solve for b

$b=-ia$

Steps for Solving Linear Equation

Divide both sides by $2+3i$. Zero divided by any non-zero number gives zero.

$$a-bi=0$$

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

$$a-ib=0$$

Subtract $a$ from both sides. Anything subtracted from zero gives its negation.

$$-ib=-a$$

Divide both sides by $-i$.

$$\frac{-ib}{-i}=-\frac{a}{-i}$$

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

$$b=-\frac{a}{-i}$$

Divide $-a$ by $-i$.

$$b=-ia$$