Difference between revisions of "Complex number"
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Revision as of 16:00, 4 April 2016
A complex number is a number that can be expressed in the form Template:Math, where Template:Math and Template:Math are real numbers and Template:Math is the imaginary unit, that satisfies the equation Template:Math.
In this expression, Template:Math is the real part and Template:Math 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 (also called Argand plane) by using the horizontal axis for the real part and the vertical axis for the imaginary part.
The complex number Template:Math can be identified with the point Template:Math 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
External links
- Complex number @ Wikipedia
