Which answer could be the result of two complex conjugates being multiplied together?(1 point)%0D%0AResponses%0D%0A%0D%0A20%0D%0A20%0D%0A%0D%0A25+4i%0D%0A25 plus 4 i%0D%0A%0D%0A16i %0D%0A16 i%0D%0A%0D%0A9−9i

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1 month ago

The multiplication of two complex conjugates can be expressed as follows: if we have two complex numbers \(a + bi\) and \(a - bi\), their product will be:

\[
(a + bi)(a - bi) = a^2 - (bi)^2 = a^2 - b^2(-1) = a^2 + b^2
\]

The result is always a real number since it is the sum of the squares of the real and imaginary parts.

Now let's analyze the options you provided:

1. **20** - This is a real number and can be a result of multiplying two complex conjugates.
2. **25 + 4i** - This has an imaginary part (4i) and thus cannot be the result of two complex conjugates being multiplied since the result must be real.
3. **16i** - This is purely imaginary and cannot be the result either.
4. **9 - 9i** - This has an imaginary part (-9i) and also cannot be the result.

Based on this analysis, the only feasible result from the options provided that could come from multiplying two complex conjugates is **20**.