complex number

number which is a combination of real and imaginary numbers, non-concrete numbers (Mathematics)

number which is a combination of real and imaginary numbers, non-concrete numbers (Mathematics)

In mathematics, a complex number is a number of the form where a and b are real numbers, and i is the imaginary unit, with the property i ² = −1. The real number a is called the real part of the complex number, and the real number b is the imaginary part. Real numbers may be considered to be complex numbers with an imaginary part of zero; that is, the real number a is equivalent to the complex number a+0i.
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Noun
1. a number of the form a+bi where a and b are real numbers and i is the square root of -1
(synonym) complex quantity, imaginary number
(hypernym) number
(hyponym) real number, real
(part-meronym) imaginary part, imaginary part of a complex number

<mathematics> A number of the form x+iy where i is the square root of -1, and x and y are real numbers, known as the "real" and "imaginary" part. Complex numbers can be plotted as points on a two-dimensional plane, known as an Argand diagram, where x and y are the Cartesian coordinates.
An alternative, polar notation, expresses a complex number as (r e^it) where e is the base of natural logarithms, and r and t are real numbers, known as the magnitude and phase. The two forms are related:
r e^it = r cos(t) + i r sin(t) = x + i y where x = r cos(t) y = r sin(t)
All solutions of any polynomial equation can be expressed as complex numbers. This is the so-called Fundamental Theorem of Algebra, first proved by Cauchy.
Complex numbers are useful in many fields of physics, such as electromagnetism because they are a useful way of representing a magnitude and phase as a single quantity.
(1995-04-10)

Complex numbers are the superset that includes all real and imaginary numbers. A complex number is usually represented by the expression a + ib where a and b are real numbers and i is the imaginary part of the expression where i has the property that i2=-1.
See also, Cross-spectrum Analysis in Time Series .