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 twodimensional 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 socalled 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.
(19950410)
Nearby terms:
complexity analysis « complexity class « complexity
measure « complex number » complex
programmable logic device » component » component
architecture
