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)
Nearby terms:
complexity analysis « complexity class « complexity
measure « complex number » complex
programmable logic device » component » component
architecture
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