18.求 e^1-i(pi)/(2),exp[(1+iπ)/4],3^i和(1+i)^i 的值.

1. $e^{1-i\frac{\pi}{2}} = e \cdot e^{-i\frac{\pi}{2}} = e \cdot (-i) = -ie$ 2. $\exp\left[\frac{1+i\pi}{4}\right] = e^{\frac{1}{4}} \cdot e^{i\frac{\pi}{4}} = \frac{\sqrt{2}}{2} e^{\frac{1}{4}} (1 + i)$ 3. $3^i = e^{i \ln 3} = \cos(\ln 3) + i \sin(\ln 3)$（主值） 4. $(1+i)^i = e^{i \ln(1+i)} = e^{-\left(\frac{\pi}{4} + 2k\pi\right)} \left[ \cos\left(\frac{\ln 2}{2}\right) + i \sin\left(\frac{\ln 2}{2}\right) \right]$，主值为 $e^{-\frac{\pi}{4}} \left[ \cos\left(\frac{\ln 2}{2}\right) + i \sin\left(\frac{\ln 2}{2}\right) \right]$ \[ \boxed{ \begin{array}{ll} 1. & -ie \\ 2. & \frac{\sqrt{2}}{2} e^{\frac{1}{4}} (1 + i) \\ 3. & \cos(\ln 3) + i \sin(\ln 3) \\ 4. & e^{-\left(\frac{\pi}{4} + 2k\pi\right)} \left[ \cos\left(\frac{\ln 2}{2}\right) + i \sin\left(\frac{\ln 2}{2}\right) \right], \text{主值: } e^{-\frac{\pi}{4}} \left[ \cos\left(\frac{\ln 2}{2}\right) + i \sin\left(\frac{\ln 2}{2}\right) \right] \\ \end{array} } \]