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

Answer 1

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.