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 \( z = a + bi \), its complex conjugate is \( \overline{z} = a - bi \). The product of a complex number and its conjugate is:
\[ z \cdot \overline{z} = (a + bi)(a - bi) = a^2 + b^2 \]
Since \( a^2 \) and \( b^2 \) are both non-negative, their sum is also non-negative.
Now, let's evaluate the given options:
- 16i - This is purely imaginary, not a non-negative real number.
- 25 + 4i - This is a complex number with a non-zero imaginary part, not a non-negative real number.
- 20 - This is a non-negative real number.
- 9 - 9i - This has an imaginary part and is not a non-negative real number.
Since the only option that matches the criteria of being a non-negative real number is 20, that is the correct answer.