1. Let points $A(-2,0), B(2,0)$, and point $P$ be on the unit circle. Then the maximum value of $|P A||P B|$ is $\qquad$
,- 1.5 .
Let point $P$ correspond to the number $z$ in the complex plane. Then
$$
\begin{array}{l}
|z|=1, \\
|P A||P B|=|z+2||z-2|=\left|z^{2}-4\right| \\
\leqslant\left|z^{2}\right|+|-4| \leqslant 5 .
\end{array}
$$

When $z=\mathrm{i}$, the equality holds.