Question

Work Out The Product Of The Following Complex Numbers: Note That A Is A Constant: I. (9−6i)(1−12i) Ii. (3a−I)(−2+14ai)

Answer 1

To find the product of complex numbers, use the distributive property and simplify the expression. The product of (9 - 6i)(1 - 12i) is -63 - 114i. The product of (3a - i)(-2 + 14ai) is 8a - 40ai.

Step-by-step explanation:

To find the product of complex numbers, we use the distributive property and multiply each term:

I. (9 - 6i)(1 - 12i) = 9(1) + 9(-12i) - 6i(1) - 6i(-12i) = 9 - 108i - 6i + 72i^2

II. (3a - i)(-2 + 14ai) = 3a(-2) + 3a(14ai) - i(-2) - i(14ai) = -6a + 42a^2i - 2i - 14ai^2

Simplifying and using the fact that i^2 = -1, we can further simplify the expressions:

I. 9 - 108i - 6i + 72i^2 = 9 - 108i - 6i - 72 = -63 - 114i

II. -6a + 42a^2i - 2i - 14ai^2 = -6a - 42ai + 2i + 14a = -6a + 14a - 42ai + 2i = 8a - 40ai