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Math Help - u(x,y) and v(x,y) satisfy the Caunchy-Riemann equations

  1. #1
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    u(x,y) and v(x,y) satisfy the Caunchy-Riemann equations

    Given the function: f(z) = z/(z-1)

    I have made it into the form:

    u(x,y) + I * v(x,y)

    Caunchy-Riemann equations are only satisfied when y=0 according to my calculations.

    Is this correct? Shoudn't the C.R equations hold everywhere except x=1 ? as from the above f(z) there is a singularity at z=1
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  2. #2
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    Re: u(x,y) and v(x,y) satisfy the Caunchy-Riemann equations

    they appear to be be satisfied everywhere though there is a pole at x=1

    u(x,y) and v(x,y) satisfy the Caunchy-Riemann equations-clipboard02.jpg
    Thanks from heatly
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  3. #3
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    Re: u(x,y) and v(x,y) satisfy the Caunchy-Riemann equations

    Thanks for that.

    I made a algebra mistake in my workings.
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