4・131 If
$$\left\{\begin{array}{l}
a^{2}+b^{2}=1, \\
c^{2}+d^{2}=1, \\
a c+b d=0
\end{array}\right.$$

Find the value of $a b+c d$.
[Solution] Multiply both sides of equation (3) by $a d+b c$, we get
$$(a c+b d)(a d+b c)=0$$

which is
$$a b\left(c^{2}+d^{2}\right)+c d\left(a^{2}+b^{2}\right)=0$$

From (1) and (2), we have $a b+c d=0$.