What is principal argument in complex numbers?

Answer: Principal argument:
The principal argument is the angle between the positive real axis and the line joining the origin and z.
The argument of a complex number z=x+iy is,
arg⁡(z=tan^-1 ⁡y / x, when x>0

arg⁡z=tan^–1 y / x+, when x<0

The principal value of an argument is denoted by Arg⁡ (^z).
The range of the value of an argument is:

arg (⁡z) ∈  Arg(⁡^z)+2πn ∣n ∈ Z

Thus,

Arg⁡(z)=ar g⁡ (⁡^z) -2πn

Hence, the value of the principal argument of the complex numbers lies in the interval (-,].