# The phase of a complex number

by eggshell
Tags: complex, number, phase
 Sci Advisor P: 820 Complex numbers don't have a "phase" they have an "argument" which is defined case by case: if z = x + iy we define $\phi = Arg(z)$ as arctan(y/x) when x > 0 arctan(y/x)+π when x < 0 and y ≥ 0 arctan(y/x)-π when x < 0 and y < 0 π/2 when x = 0 and y > 0 -π/2 when x = 0 and y < 0 indeterminate when x = 0 and y = 0.