Ans: C
$\begin{array}{rcl}
z & = & (a+5)i^6 + (a-3)i^7 \\
& = & (a+5)(-1) + (a-3)(-i) \\
& = & -(a+5) – (a-3)i
\end{array}$
$\begin{array}{rcl}
z & = & (a+5)i^6 + (a-3)i^7 \\
& = & (a+5)(-1) + (a-3)(-i) \\
& = & -(a+5) – (a-3)i
\end{array}$
Since $z$ is a real number, then the imaginary part of $z$ must be $0$. Hence, we have
$\begin{array}{rcl}
-(a-3) & = & 0 \\
a & = & 3
\end{array}$
