complex number

Noun

1.

complex number - a number of the form a+bi where a and b are real numbers and i is the square root of -1 Synonyms: complex quantity, imaginary number

(mathematics)

complex number - 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.

complex quantity, imaginary number, imaginary part, imaginary part of a complex number, number, pure imaginary number, real, real number