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 Post subject: help for two questions pleasePosted: Sun, 19 Feb 2012 21:49:57 UTC
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Joined: Tue, 29 Nov 2011 19:41:49 UTC
Posts: 13
I couldn't tackle these two problems. if you don't mind, could you help for these exercises... thanks for everything.

1-Denfie the oriented angle between two curves passing through a point in the complex plane. Show that an analytic function with non zero derivative preserves oriented angles.

2-Let be a domain in the complex plane and suppose that f is an analytic function on . Set Show that the function g denfied by is analytic in the domain

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 Post subject: Re: help for two questions pleasePosted: Sun, 19 Feb 2012 22:10:42 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
mami wrote:
I couldn't tackle these two problems. if you don't mind, could you help for these exercises... thanks for everything.

1-Denfie the oriented angle between two curves passing through a point in the complex plane. Show that an analytic function with non zero derivative preserves oriented angles.

2-Let be a domain in the complex plane and suppose that f is an analytic function on . Set Show that the function g denfied by is analytic in the domain

You should be able to find the proof of 1 in any good complex analysis book at all.

For the second one, I think you mean can you confirm this?

If that's the case then, it's easy, just look at the power series and use the Cauchy-Hadamard theorem plus the fact that is analytic on .

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 Post subject: Re: help for two questions pleasePosted: Mon, 20 Feb 2012 20:02:34 UTC
 Member

Joined: Tue, 29 Nov 2011 19:41:49 UTC
Posts: 13
Yes. You rigth. I mean
And i have a little request. Could you propose a book which i can find the proof of first question. Thanks.

mami wrote:
I couldn't tackle these two problems. if you don't mind, could you help for these exercises... thanks for everything.

1-Denfie the oriented angle between two curves passing through a point in the complex plane. Show that an analytic function with non zero derivative preserves oriented angles.

2-Let be a domain in the complex plane and suppose that f is an analytic function on . Set Show that the function g denfied by is analytic in the domain

You should be able to find the proof of 1 in any good complex analysis book at all.

For the second one, I think you mean can you confirm this?

If that's the case then, it's easy, just look at the power series and use the Cauchy-Hadamard theorem plus the fact that is analytic on .

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 Post subject: Re: help for two questions pleasePosted: Mon, 20 Feb 2012 21:01:20 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
mami wrote:
Yes. You rigth. I mean
And i have a little request. Could you propose a book which i can find the proof of first question. Thanks.

mami wrote:
I couldn't tackle these two problems. if you don't mind, could you help for these exercises... thanks for everything.

1-Denfie the oriented angle between two curves passing through a point in the complex plane. Show that an analytic function with non zero derivative preserves oriented angles.

2-Let be a domain in the complex plane and suppose that f is an analytic function on . Set Show that the function g denfied by is analytic in the domain

You should be able to find the proof of 1 in any good complex analysis book at all.

For the second one, I think you mean can you confirm this?

If that's the case then, it's easy, just look at the power series and use the Cauchy-Hadamard theorem plus the fact that is analytic on .

Ahlfors has it.

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(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

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