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Write a complex valued function in terms of z

  1. May 25, 2013 #1
    Is there a general way of writing a complex valued function
    f(z)=u(x,y)+iv(x,y) in terms of z?

    For example, suppose that I know

    f(x,y)=(x/(x^2+y^2))-i*y/(x^2+y^2)

    How do I know that it is actually f(z)=1/z?
     
  2. jcsd
  3. May 25, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    You can express x and y as function of z, but that will give really ugly formulas.

    It is useful to recognize some formulas (like x^2+y^2=|z|2 = zz* and x-iy = z*), and if those don't work you can still guess how the function could look like.
    Not every function has a nice representation like your example.
     
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