Question

Evaluate the expression (-4-2i)(3+3i)and write the result in the form a+bi
The real number a equals
The real number b equals

Answer 1

To evaluate the expression \((-4 - 2i)(3 + 3i)\), we can use the distributive property (also known as the FOIL method for binomials):

\[
(-4 - 2i)(3 + 3i) = -4 \cdot 3 + (-4) \cdot (3i) - 2i \cdot 3 - 2i \cdot (3i)
\]

Now, let's calculate each term:

1. \(-4 \cdot 3 = -12\)
2. \(-4 \cdot (3i) = -12i\)
3. \(-2i \cdot 3 = -6i\)
4. \(-2i \cdot (3i) = -6i^2\)

Recall that \(i^2 = -1\), so we can simplify \(-6i^2\):

\(-6i^2 = -6(-1) = 6\)

Now, we can combine all the terms:

\[
-12 - 12i - 6i + 6
\]

Combine the real parts and the imaginary parts:

Real part: \(-12 + 6 = -6\)
Imaginary part: \(-12i - 6i = -18i\)

So, the result is:

\[
-6 - 18i
\]

In the standard form \(a + bi\):

- The real number \(a\) equals \(-6\).
- The real number \(b\) equals \(-18\).

Thus, we have:

- **The real number a equals** \(-6\)
- **The real number b equals** \(-18\)