What is a principal argument in complex numbers?

Jillian Vang

Jillian Vang

Answered question

2022-12-25

What is a principal argument in complex numbers?

Answer & Explanation

Shea Pace

Shea Pace

Beginner2022-12-26Added 6 answers

Principal argument:
The angle formed by the positive real axis and the line connecting the origin and z is the main argument.
The argument of a complex number z=x+iy is,
argz=tan-1yx , when x>0
argz=tan-1yx+π , when x<0
The principal value of an argument is denoted by Argz.
The range of the value of an argument is:
argzArgz+2πn|nZ
Therefore,
Argz=argz2πn
Therefore, the value of the complex numbers' principal argument falls within the interval -π,π.

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