- #1

thomas49th

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Find the loci represented by

[tex] \arg(\frac{z+1}{z-1}) = \frac{\pi}{2}[/tex]

Working from inside the arg operator (it is an operator right?):

let z = x + iy

multiply num and denom by z+1

seperate into real and imag bits and you should get to

[tex] \frac{(x^{2}-1 + y^{2})-2iy}{(x-1)^{2}+y^{2}}[/tex]

Call this w

as arg(w) = arctan(Im(w)/Re(w))

[tex]\frac{2y}{x^{2}+y^{2}-1} = \tan(\frac{\pi}{2})[/tex]

but now I reach a point where my equation equals an undefined number

What should I do (or should of done)?

Thanks

Thomas

[tex] \arg(\frac{z+1}{z-1}) = \frac{\pi}{2}[/tex]

Working from inside the arg operator (it is an operator right?):

let z = x + iy

multiply num and denom by z+1

seperate into real and imag bits and you should get to

[tex] \frac{(x^{2}-1 + y^{2})-2iy}{(x-1)^{2}+y^{2}}[/tex]

Call this w

as arg(w) = arctan(Im(w)/Re(w))

[tex]\frac{2y}{x^{2}+y^{2}-1} = \tan(\frac{\pi}{2})[/tex]

but now I reach a point where my equation equals an undefined number

What should I do (or should of done)?

Thanks

Thomas

Last edited: