# How do you simplify 2/(6-4i)?

Nov 5, 2016

$\left(\frac{3}{13}\right) + \left(\frac{2}{13}\right) i$

#### Explanation:

Multiply numerator and denominator by the conjugate of the denominator.

nb: $\left(a + i b\right) \left(a - i b\right) \equiv {a}^{2} + {b}^{2}$

$\frac{2}{6 - 4 i} = \frac{2}{6 - 4 i} \times \frac{6 + 4 i}{6 + 4 i}$

$= \frac{12 + 8 i}{{6}^{2} + {4}^{2}}$

$= \frac{12 + 8 i}{52} = \left(\frac{12}{52}\right) + \left(\frac{8}{52}\right) i$

$= \left(\frac{3}{13}\right) + \left(\frac{2}{13}\right) i$