Question

What is the product of the complex numbers 3 + 4i and 6i if the options are -18 + 24i, -24 - 18i, 18 - 24i, and 24 + 18i?

a) -18 + 24i
b) -24 - 18i
c) 18 - 24i
d) 24 + 18i

Answer 1

The product of the complex numbers 3 + 4i and 6i is -24 + 18i.

Step-by-step explanation:

The product of the complex numbers 3 + 4i and 6i can be found by multiplying the real parts and the imaginary parts separately and then adding them together.

Using the distributive property, we have:

(3 + 4i)(6i) = 3(6i) + 4i(6i) = 18i + 24i²

Since i² is equal to -1, we can simplify further:

18i + 24(-1) = 18i - 24 = -24 + 18i

Therefore, the product of the complex numbers 3 + 4i and 6i is -24 + 18i, which corresponds to option b.