87 Given the complex sequence $\left\{a_{n}\right\}$ with the general term:
$$
a_{n}=(1+i)\left(1+\frac{i}{\sqrt{2}}\right)\left(1+\frac{i}{\sqrt{3}}\right) \cdots\left(1+\frac{i}{\sqrt{n}}\right)
$$

then $\left|a_{n}-a_{n+1}\right|=$
A. $\frac{\sqrt{2}}{2}$
B. $\sqrt{2}$
C. 1
D. 2
87 C. It is easy to prove by mathematical induction that $\left|a_{n}\right|=\sqrt{n+1}$. Therefore,
$$
\left|a_{n+1}-a_{n}\right|=\left|a_{n}-a_{n}\left(1+\frac{i}{\sqrt{n+1}}\right)\right|=\left|a_{n}\right| \cdot\left|\frac{i}{\sqrt{n+1}}\right|=1 .
$$