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Math Help - complex inequality

  1. #1
    Nrt
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    complex inequality

    \frac{|z-2|}{|z+3i|}<1

    I tried:

    z=x+iy

    \frac{\sqrt{(x-2)^2+y^2}}{\sqrt{x^2+(y+3)^2}}<1

    then i got stuck. I need to solve it and i think i'll have a circle equation.
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  2. #2
    Nrt
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    By the way, this is urgent. I'd be glad if you can take a look at it.
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  3. #3
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    Squaring I get 0<2x+6y+5 which an upper half-plane.
    You can see that z=0,~z=1,~z=i~\&~z=1+i all work.
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  4. #4
    Nrt
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    i think it should be 4x not 2x. But i got it, thanks.
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