Soit Gamma le segment reliant 0 à 1+2i. Calculer l'integrale $Re(z)dz.

[tex] \int\limits^{1+2i}_0 {Re(z)} \,dz= \int\limits^{1+2i}_0 {Re( \gamma ). \gamma '(t)} \, dt= \int\limits^1_0 {t(1+2i)} \, dt=(1+2i) \int\limits^1_0 {t} \, dt[/tex]
donc [tex]\int\limits^{1+2i}_0 {Re(z)}=\int\limits^1_0 {t} \, dt+2i \int\limits^1_0 {t} \, dt= \frac{1}{2}+i [/tex]