# How do you simplify (5 - 7i) (2 - 5i)?

May 29, 2016

$- 25 - 39 i$

#### Explanation:

We need to multiply each term in the first set of parentheses by each term in the second set of parentheses. We can write this as follows:

$5 \left(2 - 5 i\right) - 7 i \left(2 - 5 i\right)$

Now we distribute the $5$ and $- 7 i$. This will give us:

$10 - 25 i - 14 i + 35 {i}^{2}$

Combine like terms and remember that ${i}^{2} = - 1$ This will give us:

$10 - 39 i + 35 \left(- 1\right)$
$10 - 39 i - 35$
$- 25 - 39 i$