What is the correct way to find the argument of a complex number?

[sara_87]

Homework Statement

I have a complex number
z=1-i

I want to find the argument of this complex number

Homework Equations

The angle it makes with the positive real axis is arctan(1/1)=pi/4

The Attempt at a Solution

This point lies in the fourth quadrant of the argand diagram.

Arg(z)= angle the z makes anticlockwise with the positive real axis = 2*pi - pi/4

is 2*pi-pi/4 the correct answer?

In matlab, the argument of this number is -pi/4 so I don't understand, doesn't the argument have to always be measured anticlockwise from the positive real axis?

Thank you in advance

 

[Mark44]

Homework Statement

I have a complex number
z=1-i

I want to find the argument of this complex number

Homework Equations

The angle it makes with the positive real axis is arctan(1/1)=pi/4

The Attempt at a Solution

This point lies in the fourth quadrant of the argand diagram.

Arg(z)= angle the z makes anticlockwise with the positive real axis = 2*pi - pi/4

is 2*pi-pi/4 the correct answer?

In matlab, the argument of this number is -pi/4 so I don't understand, doesn't the argument have to always be measured anticlockwise from the positive real axis?

That might be so for positive angles, but negative angles are measured in the clockwise direction. I can't imagine that MATLAB would require all angles to be positive.

The angles 7\pi/4 and -\pi/4 are of course different, but they have the same reference point.

Thank you in advance

 

[espen180]

You can freely add multiples of 2pi to the arument of a complex number without changing its value. For different multiples of 2pi, you obtain different representations of the same argument. After all, the radian mesure is periodic in 2pi. However, there exists the notion of the principal argument (or the principal value of the argument) of a complex number. Of all the possible representations of the argument, this is the one lying between 0 and 2pi.

Therefore -pi/4 is a valid representation of arg(1-i), but it is not the principal argument. The principal argument is 7pi/4, as you stated.