Resol [1+sin(pi/8)+icos(pi/8)/1+sin(pi/8)-icos(pi/8)]^8

$$[ \frac { 1 + \sin ( \pi / 8 ) + i \cos ( \pi / 8 ) } { 1 + \sin ( \pi / 8 ) - i \cos ( \pi / 8 ) } ] ^ { 8 }$$

Calcula

$$\frac{\left(-8-6i\right)\sqrt{2\sqrt{2}+4}+\left(14+2i\right)\sqrt{\sqrt{2}+2}+14\sqrt{2}i+\left(-6+8i\right)\sqrt{4-2\sqrt{2}}+\left(2-14i\right)\sqrt{2-\sqrt{2}}-35i}{\left(-8+6i\right)\sqrt{2\sqrt{2}+4}+\left(14-2i\right)\sqrt{\sqrt{2}+2}-14\sqrt{2}i+\left(-6-8i\right)\sqrt{4-2\sqrt{2}}+\left(2+14i\right)\sqrt{2-\sqrt{2}}+35i}\approx -1+9,112560995 \cdot 10^{-17}i$$

Expandiu

$$\frac{\left(-8-6i\right)\sqrt{2\sqrt{2}+4}+\left(14+2i\right)\sqrt{\sqrt{2}+2}+14\sqrt{2}i+\left(-6+8i\right)\sqrt{4-2\sqrt{2}}+\left(2-14i\right)\sqrt{2-\sqrt{2}}-35i}{\left(-8+6i\right)\sqrt{2\sqrt{2}+4}+\left(14-2i\right)\sqrt{\sqrt{2}+2}-14\sqrt{2}i+\left(-6-8i\right)\sqrt{4-2\sqrt{2}}+\left(2+14i\right)\sqrt{2-\sqrt{2}}+35i}$$