1. Given the set $P=\left\{a_{1}, a_{2}, \cdots, a_{n}, \cdots\right\}$, and it satisfies $a_{1}=$ $1, a_{n}=a_{n-1}+4(n-1)(n \in N, n \neq 1)$. Also, the set $Q=$ $\left\{n \mid(1+i)^{2 n}=2^{n} i, n \in N\right\}$. Then the relationship between $P, Q$ is ( ).
(A) $P \subset Q$
(B) $P=Q$
(C) $P \supset Q$
(D) $P \cap Q=\varnothing$
$-1 .(\mathrm{A})$.
$$
\begin{aligned}
a_{n} & =a_{n-1}+4(n-1)=a_{n-2}+4(n-2)+4(n-1) \\
& =\cdots=a_{1}+4[(n-1)+(n-2)+\cdots+1] \\
& =1+2 n(n-1) .
\end{aligned}
$$

Since $n$ and $(n-1)$ are consecutive integers, $n(n-1)$ is an even number. Therefore, $a_{n}$ is a number of the form $4k+1$.

From $(1+i)^{2 n}=2^{*} i$ we get $2^{n} i^{n}=2^{n} i$, i.e., $i^{n}=i$. Thus, $n$ is also a number of the form $4k+1$. Therefore, $P \subset \in$.