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Complex equation 
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#1
Jan213, 01:53 PM

P: 2

Hi, I need a little help
I need to find solution for this equations: [itex]\frac{Za}{Zb}[/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. 


#2
Jan213, 03:04 PM

P: 90

Leaving it to you the conditions of existence:
[itex]Z=\frac{ab.K.\textrm{e}^{ \pm j \theta }}{1K.\textrm{e}^{ \pm j \theta }}[/itex] 


#3
Jan213, 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... 


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