233. Write the number $z=e^{a}(\cos b+i \sin b)$ in exponential form.
Solution. From the given trigonometric form of the number, we establish that $r=e^{a}$ and $\varphi=b$. Substituting these values into the exponential form of the number $z=r e^{i \phi}$, we get $z=e^{a} e^{b i}=e^{a+b i}$.