Question

multiply.
(-2 - 3i)(6 + 2i)
write your answer as a complex number in standard form.

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply each term in the first complex number by each term in the second complex number:
$$(-2)(6)+(-2)(2i)+(-3i)(6)+(-3i)(2i)$$

Step2: Simplify each term

• $(-2)(6)= -12$
• $(-2)(2i)= -4i$
• $(-3i)(6)= -18i$
• $(-3i)(2i)= -6i^{2}$ (remember that $i^{2} = - 1$)

So we have:
$$-12-4i - 18i-6i^{2}$$

Step3: Substitute $i^{2}=-1$ and combine like - terms

Substitute $i^{2}=-1$ into the expression:
$$-12-4i - 18i-6\times(-1)$$
$$-12-4i - 18i + 6$$
Combine the real parts $(-12 + 6)$ and the imaginary parts $(-4i-18i)$:
Real part: $-12 + 6=-6$
Imaginary part: $-4i-18i=-22i$
So the result is:
$$-6-22i$$

Answer:

$-6 - 22i$