If neither a nor b are equal to zero, which answer most accurately describes the product of (a + bi)(a - bi)?The real part is not positive.The imaginary part is positive.The real part is zero.The imaginary part is zero.
Accepted Solution
A:
Answer: the correct option is(D) The imaginary part is zero.Step-by-step explanation: Given that neither a nor b are equal to zero.We are to select the correct statement that accurately describes the following product :[tex]P=(a+bi)(a-bi)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]We will be using the following formula :[tex](x+y)(x-y)=x^2-y^2.[/tex]From product (i), we get[tex]P\\\\=(a+bi)(a-bi)\\\\=a^2-(bi)^2\\\\=a^2-b^2i^2\\\\=a^2-b^2\times (-1)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }i^2=-1]\\\\=a^2+b^2.[/tex]So, there is no imaginary part in the given product. Thus, the correct option is(D) The imaginary part is zero.