3.计算下列数值(a,b和φ为实常数).(1) sqrt(a+ib), (2) sqrt[3](i), (3) (2i)^i,(4) sqrt[4](2i), (5) cos(1+4i), (6) sin 5φ,(7) cos φ+cos 2φ+cos 3φ+…+cos nφ, (8) sin φ+sin 2φ+sin 3φ+…+sin nφ.

(1) $\sqrt{a+ib} = \pm \left( \sqrt{\frac{\sqrt{a^2 + b^2} + a}{2}} + i \sqrt{\frac{\sqrt{a^2 + b^2} - a}{2}} \right)$ (2) $\sqrt[3]{i} = e^{i(\pi/6 + 2k\pi/3)}$，$k=0,1,2$ (3) $(2i)^i = e^{-(\pi/2 - 2k\pi)}(\cos\ln 2 + i \sin\ln 2)$，$k \in \mathbb{Z}$ (4) $\sqrt[4]{2i} = \sqrt[4]{2} \left( \cos\left(\frac{\pi}{8} + \frac{k\pi}{2}\right) + i \sin\left(\frac{\pi}{8} + \frac{k\pi}{2}\right) \right)$，$k=0,1,2,3$ (5) $\cos(1+4i) = \cosh 4 \cos 1 - i \sinh 4 \sin 1$ (6) $\sin 5\varphi = 5 \cos^4 \varphi \sin \varphi - 10 \cos^2 \varphi \sin^3 \varphi + \sin^5 \varphi$ (7) $\sum_{k=1}^n \cos k\varphi = \frac{\sin\left(\frac{(2n+1)\varphi}{2}\right) - \sin\left(\frac{\varphi}{2}\right)}{2 \sin\left(\frac{\varphi}{2}\right)}$ (8) $\sum_{k=1}^n \sin k\varphi = \frac{\cos\left(\frac{\varphi}{2}\right) - \cos\left(\frac{(2n+1)\varphi}{2}\right)}{2 \sin\left(\frac{\varphi}{2}\right)}$ \boxed{}