Which answer could be the result of two complex conjugates being multiplied together?(1 point)

Responses

16i
16 i

25+4i
25 plus 4 i

9−9i
9 minus 9 i

20

1 answer

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 \( a + bi \), its conjugate is \( a - bi \). When you multiply them:

\[ (a + bi)(a - bi) = a^2 - (bi)^2 = a^2 + b^2 \]

where \( a^2 + b^2 \) is a non-negative real number.

Now, let's examine the given options:

  1. 16i - This is an imaginary number (not a real number).
  2. 25 + 4i - This is a complex number (not purely real).
  3. 9 − 9i - This is also a complex number (not purely real).
  4. 20 - This is a positive real number.

Therefore, the only answer that could be the result of two complex conjugates being multiplied together is:

20.