# How do you multiply (1+3i)(-4-7i)(6-5i)?

Oct 10, 2016

You can convert them into polar form and multiply them that way but I think it is just as easy to use the F.O.I.L. method (twice):

Answer: $7 - 199 i$

#### Explanation:

You can convert them into polar form and multiply them that way but I think it is just as easy to use the F.O.I.L. method (twice):

$\left(1 + 3 i\right) \left(- 4 - 7 i\right) \left(6 - 5 i\right) =$

$\left(1 + 3 i\right) \left(- 24 + 20 i - 42 i + 35 {i}^{2}\right) =$

Use ${i}^{2} = - 1$

$\left(1 + 3 i\right) \left(- 24 + 20 i - 42 i - 35\right) =$

Combine like terms:

$\left(1 + 3 i\right) \left(- 59 - 22 i\right) =$

$- 59 - 22 i - 177 i - 66 {i}^{2} =$

Use ${i}^{2} = - 1$

$- 59 - 22 i - 177 i + 66 =$

Combine like terms:

$7 - 199 i$