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Jack Rod
Jack Rod
12:48
@robjohn hi sir sorry for inviting you without notice Actually I missed my complex variable class can u please help me in getting understanding a small part of notes that i have
Jack Rod
Jack Rod
13:14
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@robjohn
why is arg z is single-valued here not defined on real axsis
robjohn
robjohn
it never says that
First of all, Arg(z) is the single-valued fuinction
and it is discontinuous on the negative real axis
nowhere does it mention "not defined"
Jack Rod
Jack Rod
why?
robjohn
robjohn
why what?
Jack Rod
Jack Rod
give me a second sir
robjohn
robjohn
I don't know what you are asking "why" about
Why is Arg single valued, or why is it discontinuous
Jack Rod
Jack Rod
13:24
if mod of z a complex is greater than zero then x/modz nd y/mod z
robjohn
robjohn
It is single valued because it is defined that way, it is discontinuous because its limit on the negative real axis is $+\pi$ from one direction and $-\pi$ from the other
Jack Rod
Jack Rod
both lie between 1,-1
robjohn
robjohn
what? neither of those last two statements make any sense with the given question.
are you mixing up modulo operator on integers with the modulus of a complex number?
I have to go for a couple of hours, I'll be back later
Jack Rod
Jack Rod
@robjohn yes
sorry i got ur point one more thing sir can i post my few more uestion here
 
2 hours later…
Jack Rod
Jack Rod
15:05
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In the next he say replace 1/3 by 1/4 and 1/5, 1/6, 1/7, by 1/8
Sir can u guide why is it so?
@robjohn
So original question is 1+1/2+1/3+......... Diverges
Prove
 
3 hours later…
robjohn
robjohn
17:56
@JackRod Sorry, I was gone a bit longer.
This is gone over in many places, here for instance.
There, each term is replaced by a smaller term in red and the smaller series can be seen to diverge.
Ping me, if this still does not make sense.

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