Integration of Complex Functions

Related: Complex Functions

Definition (Complex Integration)

Let $f:[a,b]\to \mathbb{C}$ be a bounded complex function. Since $f$ is complex, then $f(x)=u(x)+i\cdot v(x)$ where $u,v$ are real functions. Then we say that $f$ is Riemann Integrable if and only if $u,v$ are integrable. We write

$${\int }_a^{b}f(x)dx={\int }_a^{b}u(x)dx+i{\int }_a^{b}v(x)dx$$