# How do you multiply (-8i)^2?

$- 64$

#### Explanation:

Let's do this in increasingly complex bits:

There are 3 elements to what is being squared: $8 , - 1 , \mathmr{and} i$.

If we were to only have ${8}^{2}$, we'd know we'd have $8 \cdot 8 = 64$

If we were to have ${\left(- 8\right)}^{2}$, we'd know we'd have $8 \cdot 8 \cdot - 1 \cdot - 1 = 64$

But we have ${\left(- 8 i\right)}^{2}$, which means we have $8 \cdot 8 \cdot - 1 \cdot - 1 \cdot i \cdot i$.

We already know that the first four terms product to 64. So what to do with the $i$?

$i = \sqrt{- 1}$, which means that ${i}^{2} = i \cdot i = \sqrt{- 1} \cdot \sqrt{- 1} = - 1$.

And so now we can work out ${\left(- 8 i\right)}^{2} = - 64$.