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Concept

Complex Number

Analysis
Point on Real and Imaginary Axes

Every complex number can be expressed in the form a + bi, where a and b are real numbers, a is called the real part, and b is called the imaginary part, with i the imaginary unit satisfying i squared equals minus one. The impetus to study complex numbers as a topic in itself first arose in the 16th century, when Italian mathematicians found algebraic solutions for the roots of cubic and quartic polynomials. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Origin Year
1545 1
Connections

Associated With

Carl Friedrich Gauss, Mathematicians
Source Complex Number (Wikipedia)
Identity Theorem (Complex Analysis), Theorems
Open Mapping Theorem (Complex Analysis), Theorems

Attributed To

Gerolamo Cardano, Mathematicians
Source Complex Number (Wikipedia)
Niccolò Fontana Tartaglia, Mathematicians
Source Complex Number (Wikipedia)
Rafael Bombelli, Mathematicians
Source Complex Number (Wikipedia)
William Rowan Hamilton, Mathematicians
Source Complex Number (Wikipedia)

In Branch

Algebra, Branches of Mathematics
Source Complex Number (Wikipedia)
Complex Analysis, Branches of Mathematics
Source Complex Number (Wikipedia)
Sources
1. Complex Number (Wikipedia)
Wikimedia Foundation
  • lead paragraph and history section
    The impetus to study complex numbers as a topic in itself first arose in the 16th century when algebraic solutions for the roots of cubic and quartic polynomials were discovered by Italian mathematicians.
  • History section
    This conundrum led Italian mathematician Gerolamo Cardano to conceive of complex numbers in around 1545 in his Ars Magna.
  • In Branch: Algebra, Definition and basic operations
    A complex number is an expression of the form a + bi, where a and b are real numbers, and i is an abstract symbol, the imaginary unit, whose meaning will be explained further below.
  • In Branch: Complex Analysis, Complex analysis section
    The study of functions of a complex variable is known as complex analysis
  • Attributed To: William Rowan Hamilton, Lead
    A more abstract formalism for the complex numbers was further developed by the Irish mathematician William Rowan Hamilton, who extended this abstraction to the theory of quaternions
  • Attributed To: Gerolamo Cardano, Lead
    The impetus to study complex numbers as a topic in itself first arose in the 16th century when algebraic solutions for the roots of cubic and quartic polynomials were discovered by Italian mathematicians (Niccolò Fontana Tartaglia and Gerolamo Cardano)
  • Attributed To: Niccolò Fontana Tartaglia, Lead
    The impetus to study complex numbers as a topic in itself first arose in the 16th century when algebraic solutions for the roots of cubic and quartic polynomials were discovered by Italian mathematicians (Niccolò Fontana Tartaglia and Gerolamo Cardano)
  • Attributed To: Rafael Bombelli, Lead
    The rules for addition, subtraction, multiplication, and root extraction of complex numbers were developed by the Italian mathematician Rafael Bombelli
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