# How do you simplify (2+6i)(2-9i)?

Nov 30, 2015

$58 - 6 i$

#### Explanation:

You can expand the expression by multiply it or (FOIL).

Given : $\text{ } \left(2 + 6 i\right) \cdot \left(2 - 9 i\right)$

$\implies 4 - 18 i + 12 i - 54 {i}^{2}$

$\implies 4 - 6 i - 54 {i}^{2} \text{ }$ Combined like terms

Remember $\text{ } \textcolor{red}{{i}^{2} = - 1}$

Replace $- 1$ for ${i}^{2}$

$\implies 4 - 6 i - 54 \left(\textcolor{red}{- 1}\right)$
$\implies 4 - 6 i + 54$

$\implies 58 - 6 i$