Definition:Argument of Complex Number

The argument of a complex number $$z \ $$ is defined as a continuous multifunction satisfying

$$\tan \left({ \text{arg }(z) }\right) = \tfrac{\text{Im }(z)}{\text{Re }(z)} \ $$

where $$\text{Im} \ $$ is the imaginary part, and $$\text{Re} \ $$ is the real part, of $$z \ $$.