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

1 answer

When multiplying two complex conjugates together, let's denote the complex number as a+bi and its complex conjugate as abi.

The product is given by:

(a+bi)(abi)=a2(bi)2=a2b2(1)=a2+b2

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.