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powers

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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.