Complex |z-1|<|z-i| (1 Viewer)

murraysp · Mar 20, 2010

Can someone please explain to me |z-1|<|z-i|. It is a region question. I do not understand whether it is to circles simultaneously or if you sub in x+iy. Any help would be great. Thanks

ninetypercent · Mar 20, 2010

Let z = x + iy

$(x-1)^2 + y^2 < x^2 + (y-1)^2\\ x^2 - 2x + 1 + y^2 < x^2 + y^2 - 2y + 1\\ -2x + 2y < 0 \\ y < x$

This is your region

Affinity · Mar 20, 2010

you cna read that inequation as the distance of z to 1 is less than its distance to i

or z is closer to 1 than i

Complex |z-1|<|z-i| (1 Viewer)

murraysp

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ninetypercent

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