Établir les égalités suivantes :
1
\((\cos (\pi/7) + i \sin (\pi/7))(\frac{1-i\sqrt{3}}{2})(1+i) = \sqrt{2}(\cos(5\pi/84)+i\sin(5\pi/84)),\)
2
\((1-i)(\cos (\pi/5) + i \sin (\pi/5))(\sqrt{3}-i) = 2\sqrt{2}(\cos(13\pi/60)-i\sin(13\pi/60)),\)
3
\(\frac {\sqrt{2}(\cos (\pi/12) + i \sin (\pi/12))}{1+i} = \frac {\sqrt{3}-i}{2}.\)