Question

simplify.
\\((-6 - 6i)(-7i)\\)
write your answer in the form \\(a + bi\\).

Explanation:

Step1: Distribute the multiplication

We use the distributive property (also known as the distributive law of multiplication over addition) to multiply each term in the first complex number by the second complex number. So, we have:
\((-6 - 6i)(-7i)=-6\times(-7i)-6i\times(-7i)\)

Step2: Simplify each term

First, simplify \(-6\times(-7i)\):
\(-6\times(-7i) = 42i\)
Next, simplify \(-6i\times(-7i)\):
We know that \(i^2=- 1\), so \(-6i\times(-7i)=42i^{2}=42\times(-1)=-42\)

Step3: Combine the terms

Now, we combine the two simplified terms:
\(42i-42=-42 + 42i\)

Answer:

\(-42 + 42i\)