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locus of complex numbers watch

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    can some1 just verify this for me,is the locus of arg(z+i/z+2)=pi/3 this:
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    (Original post by IntegralAnomaly)
    can some1 just verify this for me,is the locus of arg(z+i/z+2)=pi/3 this:
    shouldnt it be (0,-2) and (0,-1) ?
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    oops the question is arg(z-i/z+2)=pi/3.
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    anyone?
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    if that's supposed to be a circle, then the angle certainly isnt pi/3

    and i think the two points of interest are (-2,0) and (0,-1) because you have a -i involved in there....i cant remember anything else, sorry
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    (Original post by Willa)
    if that's supposed to be a circle, then the angle certainly isnt pi/3

    and i think the two points of interest are (-2,0) and (0,-1) because you have a -i involved in there....i cant remember anything else, sorry
    no its ment to be an arc of a circle.
    If arg(z-i/z+2)=pi/3 then arg(z-i)-arg(z+2)=pi/3.So the arguement of z-i minus the arguement of z+2 is always pi/3.
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    Um, I get a Cartesian equation of the locus as:

    x^2 + 2x + x/sqrt(3) + y^2 - y - 2y/sqrt(3) + 2/sqrt(3) = 0

    Now, this can be rearranged to show it's a circle, and it does go through the point (0, 1), but from what I can tell, the centre and radius of the circle involves horrible multiples of sqrt(3) and in particular, it cuts the x-axis at some peculiar number.

    What I've said is probably *******s, but my maths isn't too hot right now.
 
 
 
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