Example 1. As shown in Figure 1, in the right triangle $\triangle OAB$, $|\overrightarrow{OA}|$ $=|\overrightarrow{AB}|$, let $z_{A}=a+bi$, find $z_{B}$.
Solve $\begin{aligned} z_{\overrightarrow{\mathrm{OC}}} & =z_{A}(\cos \theta+i \sin \theta) \\ & =\left(a+b_{i}\right)\left(\cos \frac{\pi}{2}+i \sin \frac{\pi}{2}\right) \\ & =-b+a i, \\ \therefore z_{\mathrm{B}}= & z_{\mathrm{A}}+z \overrightarrow{\mathrm{OC}} \\ = & (a-b)+(a+b) i .\end{aligned}$