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

Dec 25, 2015

$5 + 10 i$

#### Explanation:

Use the FOIL method of distribution.

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

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

$\implies - 3 + 6 i + 4 i - 8 {i}^{2}$

$\implies - 3 + 10 i - 8 {i}^{2}$

Now, recall that ${i}^{2} = - 1$. This is true since $i = \sqrt{- 1}$.

$\implies - 3 + 10 i - 8 \left(- 1\right)$

$\implies - 3 + 10 i + 8$

$\implies 5 + 10 i$