Answer
$53$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(7+2i)(7-2i)
,$ 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}
(7)^2-(2i)^2
\\\\=
49-4i^2
.\end{array}
Since $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
49-4(-1)
\\\\=
49+4
\\\\=
53
.\end{array}
