# How do you simplify (5+9i)/(5i)?

Aug 22, 2016

$\frac{9}{5} - i$

#### Explanation:

You can multiply the terms of the fraction by 5i, so that you can obtain a complex number in the standard form:

$\frac{\left(5 + 9 i\right) \cdot 5 i}{5 i \cdot 5 i} = \frac{25 i + 45 {i}^{2}}{25 {i}^{2}}$

Since ${i}^{2} = - 1$, let's substitute it:

$= \frac{25 i - 45}{-} 25$

and, in standard form:

$\frac{45}{25} - \frac{25}{25} i = \frac{9}{5} - i$