Answer
When a complex number and its conjugate are multiplied, the product will not contain the imaginary number $i.$
Work Step by Step
The product of a complex number, $a+bi,$ and its conjugate, $a-bi,$ is given by
\begin{array}{l}\require{cancel}
(a+bi)(a-bi)
\\=
(a)^2-(bi)^2
\\=
a^2-b^2(i^2)
\\=
a^2-b^2(-1)
\\=
a^2+b^2
.\end{array}
Since $a$ and $b$ are real numbers, then $a^2+b^2$ are also real numbers. Hence, the product of a real number and its conjugate is a real number.
