Question 4

Question

Integration in the complex plane.

Answer

First consider the real integral ${\int }_a^{b}f(t)dt$ along the segment $[a,b]$.

Then let $a,b\in \mathbb{R}$ and $f:[a,b]\to \mathbb{C}$ be continuous.
Then we set ${\int }_a^{b}f(t)dt:={\int }_a^b\mathrm{Re}f(t)dt+i{\int }_a^b\mathrm{Im}f(t)dt$.

Example

I don’t know if it is needed but if you want one then
[[Lecture 21 - Integration, Antiderivatives, Homotopies#]Lecture 21 - Integration, Antiderivatives, Homotopies#Integral along a Curve]