# How do you divide 5/(-5i)?

Cancel out the 5's and end up with $i$

#### Explanation:

We have:

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

We can rewrite the denominator to make it easier to work with:

$\frac{5}{- 1 \times 5 \times i}$

and to see that we can cancel out the 5 in the numerator and denominator:

$\frac{\cancel{5}}{- 1 \times \cancel{5} \times i} = \frac{1}{- i}$

And now let's clean this fraction up:

$\frac{1}{- i} = \frac{1}{- i} \left(1\right) = \frac{1}{- i} \left(\frac{i}{i}\right) = \frac{i}{- {i}^{2}} = \frac{i}{- \left(- 1\right)} = \frac{i}{1} = i$