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Complex numbers - describe geometrically

  1. Apr 30, 2008 #1

    I was just wondering if anyone would be able to help me with a question I received recently as complex numbers homework and didn't quite understand.

    There was an equation given in complex form ie. something along the lines of |z-2|=|zconjugate=2| (I cannot remember this exactly now, which I know doesn't help, but nor do I know how to convert the y=-x equation back into the given form!)

    The question then stated: "describe geometrically the relation between the line and the points (2,0) and (-2,0)" There was also a dotted line drawn through the points.

    1. The problem statement, all variables and given/known data

    "Describe geometrically the realtionship between the line and the points (2,0) and (0,-2)"

    2. Relevant equations

    3. The attempt at a solution

    Well, I didn't actually understand what 'desribe geometrically' meant, but it was obvious that the lines intersected at the point (1,-1) and that they were perpendicular to each other. The equation of the line passing through the two points is y=x-2, and I also found that if the line y=-x was reflected about the line x=1 the other graph was obtained.

    Aside from this, though, I don't actually understand what the question is asking or how I should answer it. Any help given would be greatly appreciated.

  2. jcsd
  3. Apr 30, 2008 #2


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    Staff Emeritus
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    Since you don't give the precise equation, I can't say exactly what the line should be. |z- 2| can be interpreted geometrically as the distance from z= x+ iy interpreted as the point (x,y) to (2,0). |zconjugate- 2| is the distance from (x,-y) to (2,0). Unfortunately, It is true that the distance from any point (x,y) to (2, 0) is the same as the distance from (x,-y) to (2, 0). The equation you write doesn't say anything- it is true for all points.

    Last edited: Apr 30, 2008
  4. Apr 30, 2008 #3
    ahhhh okay; thanks!

    but I'm still not sure what I should present as a solution. Does 'describe geometrically' mean in terms of equations or words?

  5. Apr 30, 2008 #4


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    Staff Emeritus
    Science Advisor

    Words. In the example I gave, the description would be "the perpendicular bisector of the line segment between (-2, 0) and (2, 0)."
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