# How do you divide (-1+3i)/(-4-8i)?

Dec 10, 2016

The answer is $= - \frac{1}{4} - \frac{1}{4} i$

#### Explanation:

When you have a division of complex numbers like

${z}_{1} / {z}_{2}$

You multiply the numerator and denominator by the conjugate of the denominator

$\frac{{z}_{1} \cdot {\overline{z}}_{2}}{{z}_{2} \cdot {\overline{z}}_{2}}$

If $z = a + i b$

Then, $\overline{z} = a - i b$

and ${i}^{2} = - 1$

$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

So,

$\frac{- 1 + 3 i}{- 4 - 8 i} = \frac{\left(- 1 + 3 i\right) \left(- 4 + 8 i\right)}{\left(- 4 - 8 i\right) \left(- 4 + 8 i\right)}$

$= \frac{4 - 8 i - 12 i + 24 {i}^{2}}{16 - 64 {i}^{2}}$

$= \frac{- 20 - 20 i}{80}$

$= - \frac{1}{4} - \frac{1}{4} i$