Question

Multiply:



left-parenthesis 2 minus 6 i right-parenthesis left-parenthesis negative 4 plus 3 i right-parenthesis

Answer options with 4 options
A.
negative 26 minus 30 i

B.
negative 26 plus 30 i

C.
10 minus 30 i

D.
10 plus 30 i

Answer 1

To multiply the complex numbers \( (2 - 6i)(-4 + 3i) \), we can use the distributive property (also known as the FOIL method).

Let's calculate it step-by-step:

1. **First terms**:
\[
2 \cdot (-4) = -8
\]

2. **Outer terms**:
\[
2 \cdot 3i = 6i
\]

3. **Inner terms**:
\[
-6i \cdot (-4) = 24i
\]

4. **Last terms**:
\[
-6i \cdot 3i = -18i^2
\]
Since \( i^2 = -1 \), we have:
\[
-18i^2 = -18(-1) = 18
\]

Now, combining all these results:
\[
-8 + 6i + 24i + 18
\]

Now, combine the real parts and the imaginary parts:
\[
(-8 + 18) + (6i + 24i) = 10 + 30i
\]

Thus, the result of the multiplication is:
\[
10 + 30i
\]

So the correct answer is option **D. \( 10 + 30i \)**.