## complex equation

Hi, I need a little help

I need to find solution for this equations:

$\frac{Z-a}{Z-b}$=K$e^{±jθ}$

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

Sorry if my post is in wrong area.

Thanks for help.
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 Leaving it to you the conditions of existence: $Z=\frac{a-b.K.\textrm{e}^{ \pm j \theta }}{1-K.\textrm{e}^{ \pm j \theta }}$
 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...

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## complex equation

How do you only get one solution when there's clearly a $\pm$ in his answer?

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