Question

multiply.
(-3 - i)(-4 + 4i)
write your answer as a complex number in standard form.

Explanation:

Step1: Apply the distributive property (FOIL method)

We multiply each term in the first complex number by each term in the second complex number:

$$
LATEXBLOCK0
$$

Step2: Simplify using \(i^2 = -1\)

Recall that \(i^2=-1\), so we substitute \(-1\) for \(i^2\) in the expression:

$$
LATEXBLOCK1
$$

Step3: Combine like terms

Combine the real parts and the imaginary parts separately:

• Real parts: \(12 + 4 = 16\)
• Imaginary parts: \(-12i + 4i = -8i\)

So the expression simplifies to \(16 - 8i\).

Answer:

\(16 - 8i\)