Complex equation

1. Jan 2, 2013

powers

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.

2. Jan 2, 2013

jfgobin

Leaving it to you the conditions of existence:

$Z=\frac{a-b.K.\textrm{e}^{ \pm j \theta }}{1-K.\textrm{e}^{ \pm j \theta }}$

3. Jan 2, 2013

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...

4. Jan 12, 2013

Char. Limit

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