Answer
$97$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(4+9i)(4-9i)
,$ use the special product on multiplying the sum and difference of like terms. Then use $i^2=-1.$
$\bf{\text{Solution Details:}}$
Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the expression above is equivalent
\begin{array}{l}\require{cancel}
(4)^2-(9i)^2
\\\\=
16-81i^2
.\end{array}
Since $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
16-81(-1)
\\\\=
16+81
\\\\=
97
.\end{array}