# How do you simplify (2-3i)(-1+4i)?

May 15, 2018

$\left(2 - 3 i\right) \left(- 1 + 4 i\right) = 10 + 11 i$

#### Explanation:

Let's use the distributive property.

$\left(2 - 3 i\right) \left(- 1 + 4 i\right) = 2 \left(- 1 + 4 i\right) - 3 i \left(- 1 + 4 i\right)$

And let's use it twice more.

$2 \left(- 1 + 4 i\right) - 3 i \left(- 1 + 4 i\right) = - 2 + 8 i + 3 i - 12 {i}^{2}$

Now remember that ${i}^{2} = - 1$.

$- 2 + 8 i + 3 i - 12 {i}^{2} = - 2 + 8 i + 3 i - 12 \left(- 1\right)$

$= - 2 + 8 i + 3 i + 12$

$= 10 + 11 i$