What is the principal argument of the complex number ?

My attempt:

However, I know this is wrong because it does not fit the inequality .

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- Oct 11th 2009, 05:15 PMViralPrincipal Argument of the Complex Number -1 + i sqrt(3)
What is the principal argument of the complex number ?

My attempt:

However, I know this is wrong because it does not fit the inequality . - Oct 11th 2009, 05:46 PMTheEmptySet
- Oct 11th 2009, 05:51 PMViral
Hmm, I'm not quite sure what you mean. Can you explain it in more details and cite proof?

- Oct 11th 2009, 06:04 PMTheEmptySet
ummm...

Well lets take an example.

Say you have the angle

and lets compare that with the angle.

.

.

So to get to the angle I would rotate all the way through radians (one around the circle so I am back where I started) then go radians.

Moral of the story.

I can go around any multiple of 2\pi radians as many times as I want and still end up in the same place. - Oct 11th 2009, 06:07 PMViral
Just to make sure, is one whole circle?

- Oct 11th 2009, 06:11 PMTheEmptySet
- Oct 11th 2009, 06:31 PMViral
I don't think this warrants another topic as it's a simple question.

The modulus argument form is . However, it could also be . How do I know which to use? - Oct 11th 2009, 06:35 PMmr fantastic
- Oct 11th 2009, 06:37 PMViral
Hmm, so the one I stated first is the only one I can use. This webpage has used both of my examples >< .

- Oct 12th 2009, 04:04 AMPlato
If