# How do you simplify (3-1i)(4+6i)?

Sep 24, 2016

$\left(3 - 4 i\right) \left(4 + 6 i\right) = 36 + 2 i$

#### Explanation:

While multiplying complex numbers, one must always remember that ${i}^{2} = - 1$

Hence $\left(3 - 4 i\right) \left(4 + 6 i\right)$

= $3 \left(4 + 6 i\right) - 4 i \left(4 + 6 i\right)$

= $3 \times 4 + 3 \times 6 i - 4 i \times 4 - 4 i \times 6 i$

= $12 + 18 i - 16 i - 24 {i}^{2}$

= $12 + 18 i - 16 i - 24 \times \left(- 1\right)$

= $12 + 18 i - 16 i + 24$

= $36 + 2 i$