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What is the product of complex conjugates? The product of complex conjugates is a difference of two squares and is always a real number. The product of complex conjugates is the same as the product of opposites. The product of complex conjugates may be written in standard form as a+bi where neither a nor b is zero. The product of complex conjugates is a sum of two squares and is always a real number.

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Answer:

Last given option is the correct answer:

"The product of complex conjugates is a sum of two squares and is always a real number."

Step-by-step explanation:

The product of two conjugates can be described and solved like this:

[tex](a + b\,i) \,(a - b\,i)= a^2-a\,b\.i+a\,b\,i-b^2\,i^2=a^2+0-b^2\,(-1)= a^2+b^2[/tex]

so, no matter what the values for the real values a and b are, the product is always a real number and the sum of two squares.

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