Complex Number: A complex number is a number that can be expressed in the form $a + bi$, where $a$ and $b$ are real numbers, and $i$ represents the imaginary unit, satisfying $i^2 = -1$.
Analytic Function: An analytic function is a complex-valued function that is locally given by a convergent power series. Analytic functions possess many desirable properties, such as differentiability and the ability to be represented by their Taylor series expansions.
Contour Integration: Contour integration is a technique in complex analysis that involves integrating a complex-valued function along a curve or contour in the complex plane. It is a powerful tool for evaluating definite integrals and solving differential equations.