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Complex equation

by powers
Tags: complex, equation
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powers
#1
Jan2-13, 01:53 PM
P: 2
Hi, I need a little help

I need to find solution for this equations:

[itex]\frac{Z-a}{Z-b}[/itex]=K[itex]e^{ąjθ}[/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.
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jfgobin
#2
Jan2-13, 03:04 PM
P: 90
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
#3
Jan2-13, 04:06 PM
P: 2
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
#4
Jan12-13, 04:02 PM
PF Gold
Char. Limit's Avatar
P: 1,943
Complex equation

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


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