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# locus of complex numbers watch

1. can some1 just verify this for me,is the locus of arg(z+i/z+2)=pi/3 this:
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2. (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) ?
3. oops the question is arg(z-i/z+2)=pi/3.
4. anyone?
5. 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
6. (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.
7. 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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