Question

Which is the value of left-parenthesis 5 plus 2 i right-parenthesis left-parenthesis 3 minus 2 i right-parenthesis?

Answer options with 5 options
A.
15

B.
23

C.
11 minus 4 i

D.
15 minus 8 i

E.
19 minus 4 i

Answer 1

To find the value of \((5 + 2i)(3 - 2i)\), we can use the distributive property (also known as the FOIL method - First, Outer, Inner, Last).

Calculating each part:

1. **First**: \(5 \times 3 = 15\)
2. **Outer**: \(5 \times (-2i) = -10i\)
3. **Inner**: \(2i \times 3 = 6i\)
4. **Last**: \(2i \times (-2i) = -4i^2\)

Now, remember that \(i^2 = -1\), so we can simplify \(-4i^2\) to \(+4\).

Now, we can sum all the parts together:
\[
15 + (-10i) + 6i + 4 = (15 + 4) + (-10i + 6i) = 19 - 4i
\]

So, the value of \((5 + 2i)(3 - 2i)\) is \(19 - 4i\).

Thus, the answer is:

**E. \(19 - 4i\)**.