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Complex equation

  1. Jan 2, 2013 #1
    Hi, I need a little help :smile:

    I need to find solution for this equations:

    [itex]\frac{Z-a}{Z-b}[/itex]=K[itex]e^{±jθ}[/itex]

    The Z is unknown and it is the complex number. The a and b is known and they are also complex numbers. K is the real number.

    I know that for [itex]-90^{°}[/itex]<θ<[itex]90^{°}[/itex] the graph in the complex plane is circle, for [itex]-45^{°}[/itex]<θ<[itex]45^{°}[/itex] the graph in the complex plane is in shape of "tomato" and for [itex]-135^{°}[/itex]<θ<[itex]135^{°}[/itex] is shape of "lens", but I don't know how to solve it.

    Sorry if my post is in wrong area.

    Thanks for help.
     
  2. jcsd
  3. Jan 2, 2013 #2
    Leaving it to you the conditions of existence:

    [itex]Z=\frac{a-b.K.\textrm{e}^{ \pm j \theta }}{1-K.\textrm{e}^{ \pm j \theta }}[/itex]
     
  4. Jan 2, 2013 #3
    In that way I got only the one solution, where are the other?
    For example, let's put b=0, K=1, theta=45°, with above formula we got only the one solution, but there is more than one solution...
     
  5. Jan 12, 2013 #4

    Char. Limit

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    Gold Member

    How do you only get one solution when there's clearly a [itex]\pm[/itex] in his answer?
     
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