# How do you simplify (7-4i)(4-i)?

Sep 9, 2016

$24 - 23 i$

#### Explanation:

We have: $\left(7 - 4 i\right) \left(4 - i\right)$

Let's expand the parentheses:

$= \left(7\right) \left(4\right) + \left(7\right) \left(- i\right) + \left(- 4 i\right) \left(4\right) + \left(- 4 i\right) \left(- i\right)$

$= 28 - 7 i - 16 i + 4 {i}^{2}$

Then, let's apply the fact that ${i}^{2} = - 1$:

$= 28 + \left(4 \cdot - 1\right) - 23 i$

$= 28 - 4 - 23 i$

$= 24 - 23 i$