
Complex Integration
Use the definition to compute the following integral:
$\displaystyle \int_C e^z$ where $\displaystyle C$ is the contour from $\displaystyle 1i$ to $\displaystyle 1+i$.
I do not see how to do this problem. I know the definition is $\displaystyle \int_C f(z)dz = \int_C f(z(t))z'(t)dt$. However, I don't see how to use it in this problem. Thanks.

The function $\displaystyle e^{z}$ is analytic $\displaystyle \forall z \in \mathbb{C}$, so that the integral...
$\displaystyle \int_{A}^{B} e^{z} \cdot dz$
... doesn't depend from the path connecting A with B...
... what is the simplest path from $\displaystyle 1  i$ to $\displaystyle 1+i$?(Itwasntme)...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$