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Centre of a circle & complex numbers

  1. Feb 19, 2013 #1
    [tex] arg(\dfrac{z}{z-2}) = \dfrac{\pi}{3} [/tex]

    sketch the locus of z and find the centre of the circle

    I've sketched the locus of z but I can't seem to find the centre of the circle. Is there a way to do it algebraically? I've attempted to use z = x + iy, but to no avail.
  2. jcsd
  3. Feb 19, 2013 #2


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    Staff: Mentor

    Can you find some (at least 3) points on the circle? The points with minimal/maximal real or imaginary part would be ideal.

    A geometric interpretation (for all points, what is the apparent angle between 0 and 2?) is nice, too.

    And if you see the symmetry of the problem, it is even better.
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