# Complex equation

by powers
Tags: complex, equation
 P: 2 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.
 P: 90 Leaving it to you the conditions of existence: $Z=\frac{a-b.K.\textrm{e}^{ \pm j \theta }}{1-K.\textrm{e}^{ \pm j \theta }}$
 PF Gold P: 1,951 Complex equation How do you only get one solution when there's clearly a $\pm$ in his answer?