complex amplitude

A complex number z may be represented as z congruent x + i y = left bracketing bar z right bracketing bar e^(i θ), where left bracketing bar z right bracketing bar is a positive real number called the complex modulus of z, and θ (sometimes also denoted ϕ) is a real number called the argument. The argument is sometimes also known as the phase or, more rarely and more confusingly, the amplitude (Derbyshire 2004, pp. 180-181 and 376). The complex argument of a number z is implemented in the Wolfram Language as Arg[z]. The complex argument can be computed as arg(x + i y) congruent tan^(-1)(y/x).

affix | argument | complex modulus | complex number | de Moivre's identity | Euler formula | imaginary part | inverse tangent | phase | phasor | real part