# Multiply the vectors. The answer is 29 - j29?

## $\left(7 + j 3\right) \left(2 - j 5\right)$

Nov 30, 2016

#### Explanation:

Use the F.O.I.L. method.

$\left(7 + j 3\right) \left(2 - j 5\right) = 14$

Add the product of the O utside terms:

$\left(7 + j 3\right) \left(2 - j 5\right) = 14 - j 35$

Add the product of the I nside terms:

$\left(7 + j 3\right) \left(2 - j 5\right) = 14 - j 35 + j 6$

Add the product of the L ast terms:

$\left(7 + j 3\right) \left(2 - j 5\right) = 14 - j 35 + j 6 - {j}^{2} 15$

Because ${j}^{2} = - 1$, the last term becomes + 15:

$\left(7 + j 3\right) \left(2 - j 5\right) = 14 - j 35 + j 6 + 15$

Combine like terms:

$\left(7 + j 3\right) \left(2 - j 5\right) = 29 - j 29$