Value of the argument (1 Viewer)

[Aysce]

According to the Terry Lee book (Page 36), it reads:

"The angle Theta is called the argument, -pi < Theta <= pi or -180 < Theta <= 180"

I don't understand why arg(z) can't equal to -pi?

 

[Shadowdude]

According to the Terry Lee book (Page 36), it reads:

"The angle Theta is called the argument, -pi < Theta <= pi or -180 < Theta <= 180"

I don't understand why arg(z) can't equal to -pi?

Isn't it so each complex number can be represented uniquely in that form?

With that restriction, each complex number becomes unique. Or else you get things like -1 = cis(pi) = cis(-pi).

 

[Trebla]

The angles pi and -pi are effectively the same on the plane

You can also define the principal argument -pi < theta < pi but it is more conventional to include pi rather than -pi.

 

[Aysce]

But why is it one or the other, why can't we have -pi >= Theta >= pi?

 

[asianese]

cispi = cis-pi. CIRCLE BABY.

 

[asianese]

But why is it one or the other, why can't we have -pi >= Theta >= pi?

There'd be an overlap. We no rike dat.

 

[Trebla]

But why is it one or the other, why can't we have -pi >= Theta >= pi?

Its just by the definition of the principal argument which serves the purpose of uniquely defining the angle within a convenient domain

 

[Aysce]

There'd be an overlap. We no rike dat.

Ah alright, cheers brah

 

[SpiralFlex]

To clarify for those, the argument of a complex number can be angle outside the restriction of theta

However the principle argument must be strictly defined with the boundary you have stated sometimes denoted as Arg(z)

 

[Shadowdude]

But why is it one or the other, why can't we have -pi >= Theta >= pi?

did you not read my post

 

[Aysce]

did you not read my post

I did haha but I was thinking along the lines of "the circle" even though yours is essentially what asianese mentioned

dw bby i wont ignore u

To clarify for those, the argument of a complex number can be angle

However the principle argument must be strictly defined with the boundary you have stated.

Oh, so within -180 < @ <= 180?

 

[Trebla]

Another way to think of it is as a 'base' of a general argument. For example for some integer k



We need to uniquely define the principal argument as the either the case where k = 0 or k = -1, not both at the same time

 

[SpiralFlex]

I did haha but I was thinking along the lines of "the circle" even though yours is essentially what asianese mentioned

dw bby i wont ignore u



Oh, so within -180 < @ <= 180?

The principle argument is that, however the argument of a complex number can be greater than 180 or less than -180

There are technically infinite arguments for a complex number, however you're after the principle argument don't use the terms intechangably

 

[Aysce]

Another way to think of it is as a 'base' of a general argument. For example for some integer k



We need to uniquely define the principal argument as the either the case where k = 0 or k = -1, not both at the same time

Oh okay, I understand

The principle argument is that, however the argument of a complex number can be greater than 180 or less than -180

There are technically infinite arguments for a complex number, however you're after the principle argument don't use the terms intechangably

Alright, I'll keep that in mind.

 

[seanieg89]

Reiterating what others have said in a different way:

Think of it as sort of like why we write



not

.

We make an arbitrary choice although there are two numbers that could be considered a square root of 1.

Analogously, there are infinitely many numbers that could be considered the "argument" of -1. One relatively convenient choice is pi, so we define that to be the principal argument.