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Complex Mapping

  1. Nov 9, 2006 #1
    w = 1/(z+2j): w = u + jv, z = x+jy

    Its not hard to express this in terms of z... z = 1/w - 2j
    But how can i go about expressing x and y and terms of u and v
    Substitution of those above terms gets you

    x + jy = 1/(u + jv) - 2j

    I am not clear on the next steps
    Any help is much appreciated.
  2. jcsd
  3. Nov 10, 2006 #2


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    Science Advisor

    Get that fraction into a+ jb form by multiplying numerator and denominator by the complex conjugate of u+ jv:
    x+ jy= (u- jv)/(u2+ v2)- 2j

    Now separate into real and imaginary parts:
    x= u/(u^2+ v^2), y= -v/(u^2+ v^2)- 2.

    (I can't tell you how much it hurt to write "j" instead of "i". Blast these engineers and their jmaginary numbers!)
  4. Nov 10, 2006 #3
    We are the infamous Electrjcal Engjneers..:tongue:
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