Answer
$153$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(12+3i)(12-3i)
,$ 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}
(12)^2-(3i)^2
\\\\=
144-9i^2
.\end{array}
Since $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
144-9(-1)
\\\\=
144+9
\\\\=
153
.\end{array}