Confirmation on Complex Numbers

[kenny_]

Hey just wanted to know if this is correct.

If Arg(w) = x
then is Arg(-3w) = Arg(-3) + Arg(w)
                        = pi + x?

[A-i-d-a-n-K]

Yes, multiply any complex number by a negative real and its argument changes by pi. Think of it like rotating it 180 degrees around the Argand diagram

[A-i-d-a-n-K]

Just be aware that you are 'removing' the negative by doing this; Arg and the r value work in conjuction. For example 2cis(pi/3)=-2cis(-2pi/3) . I always try and keep my r positive...

[Mao]

Just be aware that you are 'removing' the negative by doing this; Arg and the r value work in conjuction. For example 2cis(pi/3)=-2cis(-2pi/3) . I always try and keep my r positive...

No. This is wrong.
actually, reading your post twice, I am now totally confused about what you are trying to say. I think you have the maths correct in your head, but gave an example of 'what not to do'.
Anyhow, I'll keep this here in case anyone else gets confused.

Two things:
1. Those two things are not equal:


As you can see, not the same.

2. By convention (and definition), r is always positive.
When multiplying a complex number by a negative real number, i.e. , always try to convert the coefficient to a positive number. i.e.

[A-i-d-a-n-K]

yeah should have put the inbetween step:
-2cis(-2pi/3)=2cis(-2pi/3+pi)=2cis(pi/3)