complex equation

powers

Hi, I need a little help

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.

jfgobin

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]

powers

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...

Char. Limit

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