Math Is Fun Forum

coffeeking

Member

Registered: 2007-11-18

Posts: 44

complex function

Hi, please check if I have made any mistake.

Determine if

contain a primitive on

.

Below is my working:

has primitive

where

Since

has analytic domain

where

Therefore,

does not has a primitive on

.

Thanks in advance.

dannyv

Member

Registered: 2007-09-20

Posts: 34

Re: complex function

Hi, it seems correct, the only obscure part for me was the following:

Since

has analytic domain

But after looking at it for a couple of minutes it became clear. If you write the complex logarithm it is easier.

coffeeking

Member

Registered: 2007-11-18

Posts: 44

Re: complex function

Hi dannyv, thanks for the effort

By the way could you elaborate what do you mean by if I write the complex logarithm it is easier?

Thanks.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: complex function

coffeeking, as long as you are familiar with branch cuts, I'd say you don't need to show any more work than that.

But remember that log(z-1) has many analytic domains, depending on how you take your argument to be.  It is true though that every single one of these domains does not include C \ {1}.

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

coffeeking

Member

Registered: 2007-11-18

Posts: 44

Re: complex function

Hi Ricky thanks for the info

I have to say that there are lots of helpful helper here thanks!