# How do you divide (-5-i)/(-10i)?

Sep 12, 2016

I found: $0.5 - 0.5 i$

#### Explanation:

Here you have a division between complex numbers that normally wouldn't be immediately possible or at least will not give a complex number in standard form: $a + i b$.

To solve the problem we need to get rid of $i$ in the denominator!
To do that we multiply and divide by the complex conjugate of the denominator .

If you have a complex number, say, $3 + 4 i$ the complex conjugate is obtained changing the sign of the immaginary part as: $3 \textcolor{red}{-} 4 i$.

In our case the denominator is:
$0 - 10 i$

so the complex conjugate will be: $0 + 10 i$.

Let us multiply and divide:

$\frac{- 5 - 5 i}{0 - 10 i} \cdot \frac{0 + 10 i}{0 + 10 i} =$

After this (even if it looks more difficult) we do the multiplications:
$= \frac{- 50 i - 50 {i}^{2}}{- 100 {i}^{2}} =$

remember that ${i}^{2} = - 1$ so:

$= \frac{50 - 50 i}{100} =$

Now, the good thing is that we got rid of $i$ in the denominator AND we can rearrange separating into fractions as:
$= \frac{50}{100} - \frac{50}{100} i = 0.5 - 0.5 i = \frac{1}{2} - \frac{1}{2} i$
which is in the form $a + i b$!!!