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

1 answer

When two complex conjugates are multiplied together, their product is always a real number. This is because if we have a complex number \( z = a + bi \), its conjugate is \( \overline{z} = a - bi \). The multiplication of these two gives:

\[ z \cdot \overline{z} = (a + bi)(a - bi) = a^2 + b^2 \]

This result \( a^2 + b^2 \) is always a non-negative real number.

Now, looking at your provided options:

  1. \( 25 + 4i \) - This has an imaginary part, so it's not a product of two complex conjugates.
  2. \( 20 \) - This is a real number, so it is a possible product of two complex conjugates.
  3. \( 16i \) - This is purely imaginary, so it's not a product of two complex conjugates.
  4. \( 9 - 9i \) - This has an imaginary part, so it's not a product of two complex conjugates.

Thus, the only viable option that could result from multiplying two complex conjugates is:

20

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