Overzicht
Complex Analysis: A visual and interactive introduction
Here you can find the GeoGebra applets from the online book https://complex-analysis.github.io/
If you want to support this project, you can do it using this link: https://www.patreon.com/jcponce
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Inhoudstafel
Preliminaries
- Complex numbers: cartesian representation
- Complex numbers: Polar and exponential forms
- Complex arithmetic: geometric interpretation
- Complex Roots
- Argument and Principal argument
- Multiplication of complex numbers as stretching (squeezing) and rotation
- Polar multiplication of complex numbers
- Addition-Subtraction of complex numbers
- Explore quadratic equations
- Explore cubic equation
Functions
Mappings
Riemann surfaces: Examples
Integration
- Parametrization of curves in the complex plane
- Tangent parametrization
- Circle in the complex plane
- Circle orientation
- Complex integration: (z-1)(conj(z)^2+conj(z)+1)
- Complex integration: z^(1/2)
- Complex integration: z^i
- Complex integration: conj(z)
- Complex integration: Antiderivatives
- Exploring roots
- Visualization of the Fundametal Theorem of Algebra
- Cauchy Integral Formula: Example 2
- Cauchy-Goursat theorem: Example
Series & Taylor series
Conformal mapping