13. Among the following complex numbers $z$, $(\quad)$ has the maximum real part for $z^{5}$.
(A) -2
(B) $-\sqrt{3}+\mathrm{i}$
(C) $-\sqrt{2}+\sqrt{2}$ i
(D) 2 i
(E) $-1+\sqrt{3} i$
13. B.

Notice,
$$
\begin{array}{l}
(-2)^{5}=-32, \\
(-\sqrt{3}+i)^{5}=\left(2 e^{\frac{5 \pi}{6} i}\right)^{5} \\
=32 e^{\frac{\pi}{6} i}=16 \sqrt{3}+16 \mathrm{i} \\
\Rightarrow \operatorname{Re}(-\sqrt{3}+i)^{5}=16 \sqrt{3}, \\
(-\sqrt{2}+\sqrt{2} i)^{5}=\left(2 e^{\frac{3 \pi}{4}} i\right)^{5} \\
=32 e^{-\frac{\pi}{4} i}=16 \sqrt{2}-16 \sqrt{2} i \\
\Rightarrow \operatorname{Re}(-\sqrt{2}+\sqrt{2} i)^{5}=16 \sqrt{2}, \\
(-1+\sqrt{3} i)^{5}=2^{5}\left(e^{\frac{2 \pi}{3}} i\right)^{5} \\
=2^{5} e^{\frac{10 \pi}{3}} i=-16-16 \sqrt{3} i \\
\Rightarrow \operatorname{Re}(-1+\sqrt{3} i)^{5}=-16, \\
(2 i)^{5}=32 i \Rightarrow \operatorname{Re}(2 i)^{5}=0 .
\end{array}
$$