# How do you simplify (4+ 3i) div (2 - i)?

Jul 13, 2016

$\frac{4 + 3 i}{2 - i} = 1 + 2 i$

#### Explanation:

The complex conjugate of a complex number $a + b i$ is denoted $\overline{a + b i}$ and is given by $\overline{a + b i} = a - b i$. A useful property of the complex conjugate is that for any complex number $z$, we have $z \overline{z} \in \mathbb{R}$. We will use this property to simplify the given expression by multiplying the numerator and denominator by the conjugate of the denominator.

$\frac{4 + 3 i}{2 - i} = \frac{\left(4 + 3 i\right) \left(2 + i\right)}{\left(2 - i\right) \left(2 + i\right)}$

$= \frac{8 + 6 i + 4 i - 3}{4 + 2 i - 2 i + 1}$

$= \frac{5 + 10 i}{5}$

$= 1 + 2 i$