Question

question 9 of 10
multiply the following complex numbers:
(4 - 6i)(6 - 8i)

a. 72 + 68i
b. -24 - 68i
c. 72 - 68i
d. -24 + 68i

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first complex number by each term in the second complex number:
$$(4 - 6i)(6 - 8i)=4\times6 + 4\times(-8i)-6i\times6-6i\times(-8i)$$

Step2: Simplify each term

Calculate each product:
$$4\times6 = 24$$, $$4\times(-8i)=-32i$$, $$-6i\times6=-36i$$, $$-6i\times(-8i)=48i^{2}$$
Since \(i^{2}=-1\), then \(48i^{2}=48\times(-1)= - 48\)

Step3: Combine like terms

Combine the real parts and the imaginary parts:
Real parts: \(24-48=-24\)
Imaginary parts: \(-32i-36i=-68i\)
So, \((4 - 6i)(6 - 8i)=-24-68i\)

Answer:

B. -24 - 68i