# How do you divide 4+2i div 3-i?

Dec 29, 2015

The result is $1 + i$

#### Explanation:

To perform the division of complex numbers you have to expand the fraction by the complex conjugate of the denominator. After doing this you get a real number in the denominator.

$\frac{4 + 2 i}{3 - i} = \frac{\left(4 + 2 i\right) \left(3 + i\right)}{\left(3 - i\right) \left(3 + i\right)} = \frac{10 + 10 i}{10} = 1 + i$

Dec 29, 2015

$1 + i$

#### Explanation:

$\frac{4 + 2 i}{3 - i}$
Multiply and divide by the conjugate of the expression present in denominator i.e $3 + i$.
$\implies \frac{4 + 2 i}{3 - i} = \frac{4 + 2 i}{3 - i} \cdot \frac{3 + i}{3 + i} = \frac{12 + 4 i + 6 i + 2 {i}^{2}}{{\left(3\right)}^{2} - {\left(i\right)}^{2}}$
$= \frac{12 + 10 i - 2}{9 - \left(- 1\right)} = \frac{10 + 10 i}{9 + 1} = \frac{10 \left(1 + i\right)}{10} = 1 + i$
Hence the answer is $1 + i$.