meaning of complex number

1. 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 cost + i r sint = x + i y where x = r cost y = r sint 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.
2. a number of the form a+bi where a and b are real numbers and i is the square root of -1

Related Words

complex number | imaginary part of a complex number |

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