Summary:
The post lays as quickly as possible, some property of a complex integral.
Definition 1.1:
A contour integral of a complex function 'f' over a closed interval [a, b].:
Remarks:
- 'f' is a complex function defined as C -> C.
- The integral admits both real and imaginary parts, 'i' being the imaginary part.
LaTeX:
\begin{align*}
\int_{a}^{b} f(t)dt &= \int_{a}^{b} u(t) + iv(t)dt,\\
&= \int_{a}^{b} u(t)dt + i \int_{a}^{b} v(t)dt.
\end{align*}