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 is the imaginary unit, that satisfies the equation i2 = −1.
In this expression, a is the real part and b is the imaginary part of the complex number.
Description
Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part.
The complex number a + bi can be identified with the point (a, b) in the complex plane.
A complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number.
In this way, the complex numbers contain the ordinary real numbers while extending them in order to solve problems that cannot be solved with real numbers alone.
Applications
As well as their use within mathematics, complex numbers have practical applications in many fields, including:
History
The Italian mathematician Gerolamo Cardano is the first known to have introduced complex numbers. He called them "fictitious" during his attempts to find solutions to cubic equations in the 16th century.
See also
- Algebraic surface
- Circular motion using complex numbers
- Complex-base system
- Complex analysis
- Complex geometry
- Complex square root
- Domain coloring
- Eisenstein integer
- Euler's identity
- Gaussian integer
- Imaginary number
- Mandelbrot set
- Mathematics
- Number
- Quaternion
- Real number
- Riemann sphere (extended complex plane)
- Root of unity
- Unit complex number
External links
- Complex number @ Wikipedia
