Question

If neither a nor b are equal to zero, which answer most accurately describes the product of (a + b)(a - b)?
The product of a complex conjugate is always an imaginary number.
The product of a complex conjugate is always zero.
The product of a complex conjugate is always a mix of real and imaginary numbers.
The product of a complex conjugate is always a real number.

Answer 1

The product of a complex conjugate is always a real number. This statement is correct.

Given, if neither a nor b are equal to zero then we have to conclude that which of the following statement accurately describes the product of (a + ib)(a - ib). So, let's proceed to solve the question accordingly.

Now, solve the product of (a + ib)(a - ib), we get

(a + ib)(a - ib) = a(a - ib)+ib(a - ib)

                     = a^2-iab+iab+(ib)^2

                     = a^2+i^2b^2

we know that, i^2 = -1, then

= a^2+i^2b^2 = a^2+b^2

⇒(a + ib)(a - ib) = a^2+b^2

∴ a^2+b^2 will always give a real number.

Hence, The product of a complex conjugate is always a real number.

Therefore, option (d) is correct.

Learn more in depth about complex numbers at https://brainly.com/question/10662770

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