- #1
player1_1_1
- 114
- 0
Homework Statement
count integral: [tex]\int\limits_C\frac{e^{2z}}{z^2-4}\mbox{d}z[/tex] where [tex]C[/tex] is closed curve containing [tex]z=\pm2[/tex]
The Attempt at a Solution
[tex]\ldots=\int\limits_C\frac{e^{2z}}{(z-2)(z+2)}\mbox{d}z[/tex]
so function has two poles [tex]z=\pm2[/tex] and integral will be
[tex]\ldots=\int\limits_{C_1}\frac{e^{2z}}{(z-2)(z+2)}\mbox{d}z+\int\limits_{C_2}\frac{e^{2z}}{(z-2)(z+2)}\mbox{d}z=4\pi i[/tex]
corrrect?