Answer
$7-24i$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
(4-3i)^2
,$ use the special product on squaring binomials. Then use the equivalence $i^2=-1.$ Finally, combine combine the real parts and the imaginary parts.
$\bf{\text{Solution Details:}}$
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(4)^2-2(4)(3i)+(3i)^2
\\\\=
16-24i+9i^2
.\end{array}
Since $i^2=-1,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
16-24i+9(-1)
\\\\=
16-24i-9
.\end{array}
Combining the real parts and the imaginary parts results to
\begin{array}{l}\require{cancel}
(16-9)-24i
\\\\=
7-24i
.\end{array}
