Ans: B
$\begin{array}{rcl}
z & = & 4+5i^{10}-ki^{15}+6i^{21}+2ki^{28} \\
z & = & 4 +5i^{4\times 2 +2} -ki^{4\times 3 +3} +6i^{4\times 5+1}+2ki^{4\times 7} \\
z & = & 4 +5i^2 -ki^3 +6i +2k \\
z & = & 4 +5(-1) -k(-i)+6i +2k \\
z & = & (-1+2k) +(6+k)i
\end{array}$
For the real part and the imaginary part of $z$ are equal, we have
$\begin{array}{rcl}
-1 +2k & = & 6 +k \\
k & = & 7
\end{array}$
Hence, the real part of $z$
$\begin{array}{cl}
= & -1 +2(7) \\
= & 13
\end{array}$
