# Math Help - Complex Integration

1. ## Complex Integration

Use the definition to compute the following integral:

$\int_C e^z$ where $C$ is the contour from $1-i$ to $1+i$.

I do not see how to do this problem. I know the definition is $\int_C f(z)dz = \int_C f(z(t))z'(t)dt$. However, I don't see how to use it in this problem. Thanks.

2. The function $e^{z}$ is analytic $\forall z \in \mathbb{C}$, so that the integral...

$\int_{A}^{B} e^{z} \cdot dz$

... doesn't depend from the path connecting A with B...

... what is the simplest path from $1 - i$ to $1+i$?...

Kind regards

$\chi$ $\sigma$