Multiply the Complex Numbers below:
(3+2i)(−2+6i)
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.