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

Try to find the value of $a b+c d$.
[Solution] Multiply both sides of equation (3) by $a d+b c$, we get
$$
(a c+b d)(a d+b c)=0 \text {, }
$$

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 $a b+c d=0$.