# How do you simplify (7-2i)(2-6i)?

Multiply the quantities, take the ${i}^{2}$ quantity and work with it, and end up with
$2 - 46 i$

#### Explanation:

There are two parts to working this out: the first is working through the multiplication, and the second is dealing with $i$.

So let's do the multiplication first:

$7 \cdot 2 = 14$
$7 \cdot - 6 i = - 42 i$
$- 2 i \cdot 2 = - 4 i$
$- 2 i \cdot - 6 i = 12 {i}^{2}$

Let's now talk about $i$

$i = \sqrt{- 1}$, so when we have ${i}^{2}$, we end up with $\sqrt{- 1} \cdot \sqrt{- 1} = - 1$. Which means we can take the $12 {i}^{2}$ term and simplify it to

$12 {i}^{2} = 12 \cdot - 1 = - 12$

Now let's combine our new results from the multiplication:

$14 - 12 = 2$
$- 42 i - 4 i = - 46 i$

Since we can't do anything further with $i$ and the real term and the imaginary terms can't combine, we are left with a final answer of

$2 - 46 i$