# How do you multiply (5-3i)(-8+5i)?

Oct 31, 2016

$\left(5 - 3 i\right) \left(- 8 + 5 i\right) = - 25 + 49 i$

#### Explanation:

We must use the distributive property to expand these two binomials:

$\left(5 - 3 i\right) \left(- 8 + 5 i\right)$
$= - 40 + 25 i + 24 i - 15 {i}^{2}$

Note that ${i}^{2} = \sqrt{-} 1 \cdot \sqrt{-} 1 = - 1$

$= - 40 + 49 i - 15 \left(- 1\right)$
$= - 40 + 15 + 49 i$
$= - 25 + 49 i$

Remember the answer must be in the form $a + b i$ where a is a constant and b is the coefficient on the $i$ term.

$\therefore \left(5 - 3 i\right) \left(- 8 + 5 i\right) = - 25 + 49 i$