Locus of complex number

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Hello! Few weeks ago we started learning complex number. And i have some questions about that because not all i understand and also dont know if my solution is good :)
Also dont know if my name of topic is good :) if something goes wrong just say. I'd be grateful

My task: |(z+1)/(z-1)|=3 need to calculate and graph that.
I know that modulus of complex number z=x+yi is equal to |z|=√x^2+y^2

The same i tried to do in my exercise.
|(z+1)/(z-1)|=3
[itex]\sqrt{(x+1)^2+y^2/(x-1)^2+y^2}=3[/itex] then i sqaured both sides
[itex](x+1)^2+y^2/(x-1)^2+y^2=9[/itex]
[itex](x+1)^2+y^2=9((x-1)^2+y^2))[/itex]
[itex]x^2+2x+1+y^2=9x^2-18x+9+9y^2[/itex]
[itex]8x^2-20x+8+8y^2=0[/itex]
[itex]x^2+1+y^2=(20x/8)[/itex]
[itex]x^2+y^2=(20x/8)-1[/itex]
And thats it what i done. For real i have no idea how graph that and not sure if this solution is good. Thanks for advise what i need to do next or correct my mistakes :)

P.S. I think this is a circle, but dont know where is center and what is radius.
 
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Answers and Replies

  • #2
Curious3141
Homework Helper
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Hello! Few weeks ago we started learning complex number. And i have some questions about that because not all i understand and also dont know if my solution is good :)
Also dont know if my name of topic is good :) if something goes wrong just say. I'd be grateful

My task: |(z+1)/(z-1)|=3 need to calculate and graph that.
I know that modulus of complex number z=x+yi is equal to |z|=√x^2+y^2

The same i tried to do in my exercise.
|(z+1)/(z-1)|=3
[itex]\sqrt{(x+1)^2+y^2/(x-1)^2+y^2}=3[/itex] then i sqaured both sides
[itex](x+1)^2+y^2/(x-1)^2+y^2=9[/itex]
[itex](x+1)^2+y^2=9((x-1)^2+y^2))[/itex]
[itex]x^2+2x+1+y^2=9x^2-18x+9+9y^2[/itex]
[itex]8x^2-20x+8+8y^2=0[/itex]
[itex]x^2+1+y^2=(20x/8)[/itex]
[itex]x^2+y^2=(20x/8)-1[/itex]
And thats it what i done. For real i have no idea how graph that and not sure if this solution is good. Thanks for advise what i need to do next or correct my mistakes :)

P.S. I think this is a circle, but dont know where is center and what is radius.

You're on the right track. It is a circle. Keep all the terms on the left hand side (LHS), complete the square for x. Finally, move the constant over to the RHS, then compare with the standard equation for the circle.
 

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