Re: Complex Analysis - I make a mistake somewhere.
From: Brian VanPelt (bvanpelt_at_neo.rr.com)
Date: 09/13/04
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Date: Mon, 13 Sep 2004 01:26:47 GMT
On Mon, 13 Sep 2004 00:35:25 +0000 (UTC), "<none@mathforum.org ("Me)
wrote:
>Hello. I have a book about Complex Analysis and I try to solve an example alone using function derivate elementary formula. Could somebody notify ma an attention where I make a mistake?
>
>I use the formula:
>
>f'(z0) = lime[dz->0] (f(z0+dz) - f(z0))/dz
>
>The example in my book is:
>
>f(z) = (iz+z)^2
>
>it needs to be the first derivate calculated. f'(z).
>
>This is the problem. I obviously make a mistake somewhere so I do not take the proper result.
>
>The result needs to be the following:
>
>f(z) = (iz+z)^2
>f'(z) = 4i - 2z
>
>my first establishments I tried were:
>
>f'(z) = ((iz+z) + dz)^2 - (iz+z)^2)/dz
>
>f'(z) = ((iz+z + dz)^2 - (iz+z)^2)/dz
>
Right here is the mistake. If f(z) = ( iz + z)^2, then
f(z + dz) = ( i(z + dz) + z + dz)^2
you forgot to replace every instance of z with z + dz.
Also, you can write ( iz + z)^2 = z^2 ( i + 1)^2. It seems a little
easier to me, and then
f(z + dz) = (z + dz)^2 ( i + 1)^2
>any of them does not give the proper solution. Could somebody notify me a mistake I make?
>
>Thanks.
Hope this helps,
Brian
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