Live briefing
Everything about Complex plane
Geometric representation of the complex numbers
In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal x-axis, called the real axis, is formed by the real numbers, and the vertical y-axis, called the imaginary axis, is formed by the imaginary numbers. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Complex planeA 5-minute orientation
- Skim a recent paper: Flexible Intelligent Sensing System for Plane Complex Strain MonitoringInfluential work since 2022
- Pick up a classic book: Komplexe Zahlen und ebene GeometrieThe most-reprinted book on the subject
- Read the landmark paper: Level repulsion in the complex planeCited 68 times
- Go sideways: Branch pointA closely related topic
- Go sideways: Complex logarithmA closely related topic
📖 Definitions
Noun A representation of the space of complex numbers.
🏆 Landmark papers (most cited)
Level repulsion in the complex plane
Hamiltonian maps in the complex plane
The 9-vertex complex projective plane
Strange objects in the complex plane
Hybrid inflation in the complex plane
Triangle formulas in the complex plane
Fractal “Aggregates” in the Complex Plane
Anisotropy of plane complex elastic bodies
🆕 Influential since 2022
📚 Books worth reading
Komplexe Zahlen und ebene GeometrieJoachim Engel · 2009
A treatise on algebraGeorge Peacock · 1842
Complex analysisIan Stewart, David Orme Tall · 1983- 📕Mnimosti v geometriiPavel Florensky · 1985
- 📕Mappings of the plane, with applications to trigonometry and complex numbersH. E. Chrestenson · 1966
- 📕Mappings of the planeH. E. Chrestenson · 1966
- 📕A Practical CalculusAlec Grenville Proudfoot · 1960
- 📕Plane trigonometry and complex numbersDušan Jevtić · 2010
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Branch point In the mathematical field of complex analysis, a branch point of a multivalued function is a point such that if the function is n-valued (has n values)…
- Complex logarithm In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which…
- Argument (complex analysis) In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and…
- Contour integration In complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane. Contour integration is used to study…
- Inverse trigonometric functions In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions…
- Euler's formula Euler's formula is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the…
- Möbius transformation In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form f(z)=az+bcz+d of one complex variable…
- Unit circle In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle…