When multiplying two complex conjugates together, let's denote the complex number as \( a + bi \) and its complex conjugate as \( a - bi \).
The product is given by:
\[ (a + bi)(a - bi) = a^2 - (bi)^2 = a^2 - b^2(-1) = a^2 + b^2 \]
This outcome yields a real number, specifically the sum of the square of the real part and the square of the imaginary part. Thus, the result of multiplying two complex conjugates is always a real number.
Now, let’s assess the responses for real numbers:
- 25 + 4i (not real)
- 16i (not real)
- 20 (real)
- 9 - 9i (not real)
The only response that is a real number is 20. Therefore, the result of two complex conjugates being multiplied together could be 20.
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