We haven't been given the definition. One of the other problems left in this problem set is to come up with a definition of a closure interms of a line R where R is all real numbers
I get that it's not closed since the set is open, with < as opposed to <=, but I don't understand how a set that is open, can still have a closure. I have a hard time picturing that. I do agree with the rest however.
I suppose the boundary would be the set it's self, -pi<arg(z)<pi or would that...
The closure of E is the the boundary of the closed set along with the inner regions, I thought. We haven't fully defined a closure in class, which is why I was unsure as to why this is classified as a closed set if it goes on forever everywhere when arg(z) doesn't equal pi+2kpi.
pi/2 brings the angle to the imaginary axis and another pi/2 you're asking? It would bring it back down to the real axis at +pi. I don't understand what you're saying about the arg of those numbers. Isn't it just 0 to pi/2 to get to the imaginary axis and another pi/2 to get back down to the...
From the real axis to the imaginary axis it would be from 0 to 0+90i or 0+pi/2 i? and from the imaginary axis back down to the real axis would it be pi or 180 + 0i?
We haven't really covered what arg(z) is equivalent too. I know it's the angle, but we never went over how to find the z value within arg(z). I looked it up and it says it's equivalent to atan (imag(z)/real(z)), but I've never heard of atan, so I'm lost there too. Can't you specify the closure...