Question

Multiply and write the product as a complex number in standard form.

Answer 1

$8-14i$

1) In this problem, we need to remember that the imaginary number has this equivalence:

$i^2=-1$

2) So, let's multiply those factors distributing the factor (FOIL):

$\begin{gathered} (4-2i)(3-2i) \\ \left(4\cdot \:3-\left(-2\right)\left(-2\right)\right)+\left(4\left(-2\right)+\left(-2\right)\cdot \:3\right)i \\ (12-4)+(-8-6)i \\ 8-14i \end{gathered}$

That equivalence allows us to simplify this expression. So we can write this as the answer:

$8-14i$