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Complex Analysis Basics

★★★★☆Undergraduate

📖Definition

Complex analysis studies calculus of complex-valued functions. Analytic functions are differentiable and have beautiful properties.

e^iθ = cosθ + isinθ

Euler's formula

(∂ u)/(∂ x) = (∂ v)/(∂ y), (∂ u)/(∂ y) = -(∂ v)/(∂ x)

Cauchy-Riemann equations

∮_C f(z) dz = 0

Cauchy's integral theorem (simply connected)

예제 1

Calculate e^(iπ) using Euler's formula.

Discovered by: Leonhard Euler, Augustin-Louis Cauchy (18th-19th century)

Euler discovered the formula; Cauchy systematized complex function theory.

AC circuit analysis

2D flow

Wave functions

#복소해석#오일러#complex analysis#Euler