# How do you simplify (8i)(-4i)?

Mar 17, 2018

$32$

#### Explanation:

When performing the basic mathematical functions on terms that contain $i$ within them, it is easiest to recognize it as a variable when starting off.

We can begin to treat this as a normal multiplication problem:

$\left(8 i\right) \left(- 4 i\right)$

$= - 32 {i}^{2}$

Now that we have this, we need to understand how setting $i$ to a power other than $1$ changes the value.

${i}^{0} = 1$
${i}^{1} = \sqrt{- 1}$
${i}^{2} = - 1$
${i}^{3} = - i$
${i}^{4} = 1$
${i}^{5} = \sqrt{- 1}$
$\ldots$

In this instance, however, the ${i}^{2}$ would then become $- 1$.

Knowing this we can write our expression as:

$- 32 \left(- 1\right)$

$= 32$

Mar 17, 2018

$32$

#### Explanation:

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{w h i t e}{x} {i}^{2} = {\left(\sqrt{- 1}\right)}^{2} = - 1$

$\Rightarrow \left(8 i\right) \left(- 4 i\right)$

$= - 32 {i}^{2} = - 32 \times - 1 = 32$