Résoudre :
1
\((z+1)^n = (z-1)^n\).
2
\((z+1)^n = z^n = 1\).
3
\(z^4 - z^3 + z^2 - z + 1 = 0\).
4
\(1 + 2z + 2z^2 + \dots + 2z^{n-1} + z^n = 0\).
5
\(\left(\frac{1+ix}{1-ix}\right)^n = \frac{1+i\tan a}{1-i\tan a}\).
6
\(\overline x = x^{n-1}\).
7
\(\left(\frac{z+1}{z-1}\right)^3 + \left(\frac{z-1}{z+1}\right)^3 = 0\).