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

Dec 17, 2015

Multiply both numerator and denominator by the Complex conjugate of the denominator to find:

$\frac{2 - 3 i}{3 + 4 i} = - \frac{6}{25} - \frac{17}{25} i$

#### Explanation:

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

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

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

$= \frac{\left(6 - 12\right) - \left(9 + 8\right) i}{9 + 16}$

$= \frac{- 6 - 17 i}{25}$

$= - \frac{6}{25} - \frac{17}{25} i$