1. Let the complex number $z$ satisfy $|z|=1$. Then the maximum value of $\mid z^{3}+3 z+2 \mathrm{i}$ is ( ).
(A) $4 \sqrt{2}$
(B) $3 \sqrt{3}$
(C) $2 \sqrt{5}$
(D) $4 \sqrt{3}$
-.1. B.
Let's assume $z=a+bi$ from the given conditions.
Thus, $a^{2}+b^{2}=1$.
Then, $z^{3}+3z+2i=4a^{3}-\left(4b^{3}-6b-2\right)i$.
Therefore, $\left|z^{3}+3z+2i\right|^{2}=\left(4a^{3}\right)^{2}+\left(4b^{3}-6b-2\right)^{2}$ $=-16b^{3}-12b^{2}+24b+20$.
It is easy to see that when $b=\frac{1}{2}$, the above expression reaches its maximum value of 27.
Thus, the maximum value sought is $3\sqrt{3}$.