Question

If neither a nor b are equal to zero, which answer most accurately describes the product of (a + bi)(a - bi)?

The imaginary part is zero.
The real part is zero.
The imaginary part is positive.
The real part is not positive.

Answer 1

The imaginary part is zero.

Explanation:

we know that

Applying the difference of squares formula

`a^2-bi^2=(a+bi)(a-bi)`

Remember that

`i^(2)=-1`

substitute

`a^2-bi^2=a^2-b^2(-1)=a^2+b^2`

therefore

The imaginary part is zero.