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

Dec 8, 2015

$5 - i$

#### Explanation:

Use the FOIL method.

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

$= 2 - 3 i + 2 i - 3 {i}^{2}$

$= 2 - i - 3 {i}^{2}$

While this may appear to be as simplified as possible, it's not.

Since $i = \sqrt{- 1}$, it's also true that ${i}^{2} = - 1$. Because of this, we can replace the ${i}^{2}$ with $- 1$.

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

$= 2 - i + 3$

$= 5 - i$