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Re: Derivative of g(z) = Arg(z) and f(z) = Re(z) + Im(z)?

• To: mathgroup at smc.vnet.net
• Subject: [mg54136] Re: Derivative of g(z) = Arg(z) and f(z) = Re(z) + Im(z)?
• From: highegg at centrum.cz (highegg)
• Date: Fri, 11 Feb 2005 03:34:06 -0500 (EST)
• References: <xglsxn7ymm4h@legacy>
• Sender: owner-wri-mathgroup at wolfram.com

On 9 Feb 05 13:59:53 -0500 (EST), Marie wrote:
>How do I solve a derivative of a complex function Arg(z) or Re(z) +
>Im(z) by definition? (f(z) - f(w))/(z-w) -> f'(w) as z->w... 

hello,
function like Re(z)+Im(z) or Arg(z) do not have a complex derivative
(we say they're non-holomorphic), because they don't satisfy the
Cauchy-Riemann conditions.

http://mathworld.wolfram.com/Cauchy-RiemannEquations.html