Question

(8 - 4i)(5 - 3i)

Explanation:

Step1: Use the distributive property (FOIL method)

Multiply each term in the first complex number by each term in the second complex number:
$$(8 - 4i)(5 - 3i)=8\times5+8\times(-3i)+(-4i)\times5+(-4i)\times(-3i)$$

Step2: Simplify each product

Calculate each term:
$$8\times5 = 40$$
$$8\times(-3i)=-24i$$
$$(-4i)\times5=-20i$$
$$(-4i)\times(-3i)=12i^{2}$$
So the expression becomes:
$$40 - 24i - 20i+12i^{2}$$

Step3: Combine like terms and use \(i^{2}=- 1\)

Combine the imaginary terms \(-24i-20i=-44i\), and substitute \(i^{2}=-1\) into \(12i^{2}\):
$$40-44i + 12\times(-1)$$
$$=40-44i-12$$

Step4: Combine the real terms

Combine \(40 - 12\):
$$28-44i$$

Answer:

\(28 - 44i\)