Question

Which answer could be the result of two complex conjugates being multiplied together?(1 point)
Responses

16i
16 i

25+4i
25 plus 4 i

9−9i
9 minus 9 i

20

Answer 1

When two complex conjugates are multiplied together, the result is always a non-negative real number. This is because if you have a complex number \( a + bi \), its conjugate is \( a - bi \). When you multiply them:

\[
(a + bi)(a - bi) = a^2 - (bi)^2 = a^2 + b^2
\]

where \( a^2 + b^2 \) is a non-negative real number.

Now, let's examine the given options:

1. **16i** - This is an imaginary number (not a real number).
2. **25 + 4i** - This is a complex number (not purely real).
3. **9 − 9i** - This is also a complex number (not purely real).
4. **20** - This is a positive real number.

Therefore, the only answer that could be the result of two complex conjugates being multiplied together is:

**20**.