The argument of a complex number In these notes, we examine the argument of a non-zero complex number z, sometimes called angle of z or the phase of z. Following eq. (4.1) on p. 49 of Boas, we write: z = x+iy = r(cosθ +isinθ) = reiθ, (1) where x = Re z and y = Im z are real numbers. The argument of z is denoted by θ, which is measured in
Worked Examples. Example 1. Find the modulus and argument of the complex number z = 3+2i z = 3 + 2 i. Solution. |z| = √32+22 = √9 +4 = √13 | z | = 3 2 + 2 2 = 9 + 4 = 13. As the complex number lies in the first quadrant of the Argand diagram, we can use arctan 2 3 arctan 2 3 without modification to find the argument.
This is a real number, but this tells us how much the i is scaled up in the complex number z right over there. Now, one way to visualize complex numbers, and this is actually a very helpful way of visualizing it when we start thinking about the roots of numbers, especially the complex roots, is using something called an Argand diagram.
Arg [z] is left unevaluated if z is not a numeric quantity. Arg [z] gives the phase angle of z in radians. The result from Arg [z] is always between and . Arg [z] has a branch cut discontinuity in the complex z plane running from to 0. Arg [0] gives 0. Arg can be used with Interval and CenteredInterval objects. » Arg automatically threads over
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what is arg z of complex number
