Question

simplify.
(8 - 2i)(-3i)
write your answer in the form a + bi.

Explanation:

Step1: Distribute -3i to each term

Using the distributive property (also known as the distributive law of multiplication over addition), we multiply \(-3i\) with each term inside the parentheses \((8 - 2i)\). So we have:
\(8\times(-3i)+(-2i)\times(-3i)\)

Step2: Simplify each product

First, simplify \(8\times(-3i)\):
\(8\times(-3i)= -24i\)
Then, simplify \((-2i)\times(-3i)\). Remember that \(i^2=- 1\), so:
\((-2i)\times(-3i)=(-2)\times(-3)\times i\times i = 6i^{2}=6\times(-1)=-6\)

Step3: Combine the results

Now we combine the two simplified terms from Step 2. We have \(-24i-6\). We can rewrite this in the form \(a + bi\) by rearranging the terms:
\(-6-24i\)

Answer:

\(-6 - 24i\)