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Geometric reps of complex formula

  1. Jan 20, 2008 #1
    1. The problem statement, all variables and given/known data
    Describe geometrically the sets of points determined by the relations:

    a) |z-i|+|z-1| = 2
    b) |z-i|=|z+1|
    c) Re z = |z-2|

    2. Relevant equations



    3. The attempt at a solution

    I know the answer of a is suppose to be Ellipse with foci at i and 1, major axis 2
    and b is Perpendicular bisector of the line segment connecting z=i and z = -1
    and c is Parabola focus at z=2, directrix the imaginary axis (from the back of the book), but could one of you help me to see how the author got those answers?
     
  2. jcsd
  3. Jan 20, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    The most direct way to handle all of them is to put z=x+iy and look at the x,y equations. You could also look up the geometric definition of an ellipse and a parabola to do those more directly.
     
  4. Jan 20, 2008 #3
    Yep. The direct method worked. Thanks.
     
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