Modulus: It is defined as
Argument: Arg(Z): It is defined as
it is also known as amplitude of Z symbolically amp(Z)
Note:

If Z=0 then x=0 and y=0

The Argument θ of a complex number is not unique.

If θ be the value of argument so also is 2nπ + θ where n=0,± 1, ±2,…
Principal Value Argument.: The value of argument which satisfy the inequality