Multiply the Complex Numbers below:

Question

(3+2i)(−2+6i)

Answer 1

To multiply the complex numbers (3+2i)(−2+6i), we will use the FOIL method.

(3+2i)(−2+6i) = 3*(-2) + 3*(6i) + 2i*(-2) + 2i*(6i)

Simplifying each term, we get:

= -6 + 18i - 4i + 12i^2

Since i^2 is equal to -1, we can substitute -1 for i^2:

= -6 + 18i - 4i + 12(-1)

Simplifying further:

= -6 + 18i - 4i - 12

= -18 + 14i

So, the product of (3+2i)(−2+6i) is -18 + 14i.