# How do you simplify (5+3i)(3-i)?

Jul 30, 2016

$\left(5 + 3 i\right) \left(3 - i\right) = 18 + 4 i$

#### Explanation:

When we exercise arithmetic operations using complex numbers, particularly multiplication and / or division, one thing which needs to be remembered is that ${i}^{2} = - 1$

Hence $\left(5 + 3 i\right) \left(3 - i\right)$

= $5 \times 3 - 5 \times i + 3 i \times 3 + 3 i \times \left(- i\right)$

= $15 - 5 i + 9 i - 3 {i}^{2}$

= $15 - 5 i + 9 i - 3 \left(- 1\right)$

= $15 - 5 i + 9 i + 3$

= $18 + 4 i$