Question

Which answer could be the result of two complex conjugates being multiplied together?(1 point) Responses 25+4i 25 plus 4 i 20 20 16i 16 i 9−9i

Answer 1

When two complex conjugates are multiplied together, their product is always a real number. This is because if we have a complex number \( z = a + bi \), its conjugate is \( \overline{z} = a - bi \). The multiplication of these two gives:

\[
z \cdot \overline{z} = (a + bi)(a - bi) = a^2 + b^2
\]

This result \( a^2 + b^2 \) is always a non-negative real number.

Now, looking at your provided options:

1. \( 25 + 4i \) - This has an imaginary part, so it's not a product of two complex conjugates.
2. \( 20 \) - This is a real number, so it is a possible product of two complex conjugates.
3. \( 16i \) - This is purely imaginary, so it's not a product of two complex conjugates.
4. \( 9 - 9i \) - This has an imaginary part, so it's not a product of two complex conjugates.

Thus, the only viable option that could result from multiplying two complex conjugates is:

**20**