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Homework Help: Functions of a Complex Variable

  1. Jan 8, 2012 #1
    Hi guys. Please help me with this.

    Consider the Mapping:

    w = 1/(z-j)

    questions:(1) Write z as a function of w.

    (2) Express X and Y in terms of u and v.

    (3) Find and describe the image of the line x = 1 under this mapping.

    2. Relevant equations --

    w = u+jv
    z = x+jy

    3. The attempt at a solution

    I dont understand the first question and have no idea of how to have it as a function of w. However I do understand from then onwards as to express in terms u and v.
  2. jcsd
  3. Jan 8, 2012 #2


    User Avatar
    Science Advisor

    It's strange that you should be working with complex number and not understand something from basic algebra.
    [tex]w= \frac{1}{z- j}[/tex]
    [tex]z- j= \frac{1}{w}[/tex]
    [tex]z= \frac{1}{w}+ j[/tex]
  4. Jan 8, 2012 #3
    Thank you.

    That is really simple. Probably that is why i was confused as I did not thought it would be that simple.

    Thanks alot!!
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