# How do you simplify (7+2i )/( 4+5i)?

Jul 26, 2016

$\frac{38}{41} - \frac{27}{41} i$

#### Explanation:

You can multiply numerator and denominator by the same expression $4 - 5 i$

$\frac{\left(7 + 2 i\right) \left(4 - 5 i\right)}{\left(4 + 5 i\right) \left(4 - 5 i\right)}$

$\frac{28 - 35 i + 8 i - 10 {i}^{2}}{16 - 25 {i}^{2}}$

Since ${i}^{2} = - 1$, you have:

$\frac{28 - 27 i + 10}{16 + 25}$

$\frac{38 - 27 i}{41}$

$\frac{38}{41} - \frac{27}{41} i$