Complex Number

A complex number can be visually represented using a two-dimensional Cartesian coordinate system as an ordered pair of real numbers on the complex plane. The representation of a complex number in terms of its Cartesian coordinates in the form , where is the imaginary unit, is called the algebraic form of that complex number. The coordinate is called the real part and the imaginary part of the complex number, respectively. The absolute value (or the modulus) of a complex number is defined by .

Alternatively to the Cartesian system, the polar coordinate system may used. In polar coordinates , the radial coordinate and the angular coordinate , where , is called the argument (or angle) of the complex number . A complex number is then represented in the trigonometric form , or in the exponential form . In technical applications the argument is often chosen from the interval and it is called phase. The corresponding exponential form is then called phasor form.