SilverTan SilverTan

10-10-2017
Mathematics

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Find the loci for the complex numbers that satisfy[tex]|z-1|=|z+1|[/tex]

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LammettHash LammettHash

10-10-2017

Let [tex]z=x+iy[/tex]. Then

[tex]|z-1|=\sqrt{(x-1)^2+y^2}[/tex]
[tex]|z+1|=\sqrt{(x+1)^2+y^2}[/tex]
[tex]\implies (x-1)^2+y^2=(x+1)^2+y^2[/tex]
[tex]\implies (x-1)^2=(x+1)^2[/tex]
[tex]\implies -2x=2x[/tex]
[tex]\implies x=0[/tex]

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