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Soit \(\beta \in \Cc\) tel que \(\beta^7=1\) et \(\beta \not=1\). Montrer \[{\beta \over 1+ \beta^2} + {\beta^2 \over 1+ \beta^4} + {\beta^3 \over 1+ \beta^6} =-2\]
Soit \(\beta \in \Cc\) tel que \(\beta^7=1\) et \(\beta \not=1\). Montrer \[{\beta \over 1+ \beta^2} + {\beta^2 \over 1+ \beta^4} + {\beta^3 \over 1+ \beta^6} =-2\]