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Math Help - Argand Plane?

  1. #1
    Super Member fardeen_gen's Avatar
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    Argand Plane?

    If \sum_{r = 1}^{4} a_{r} = 0 and \sum_{r = 1}^{4} a_{r}Z_{r} = 0 where a_{1},a_{2},a_{3},a_{4} are non-zero real numbers and P(Z_{1}),Q(Z_{2}),R(Z_{3}), S(Z_{4}) are concyclic points on Argand Plane, then prove that:
    \sum_{r = 1}^{4} a_{r}|Z_{r}|^2 = 0.48
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    Quote Originally Posted by fardeen_gen View Post
    If \sum_{r = 1}^{4} a_{r} = 0 and \sum_{r = 1}^{4} a_{r}Z_{r} = 0 where a_{1},a_{2},a_{3},a_{4} are non-zero real numbers and P(Z_{1}),Q(Z_{2}),R(Z_{3}), S(Z_{4}) are concyclic points on Argand Plane, then prove that:
    \sum_{r = 1}^{4} a_{r}|Z_{r}|^2 = 0.48
    This cannot be correct. Suppose that a_{1},a_{2},a_{3},a_{4} and Z_{1},Z_{2},Z_{3},Z_{4} satisfy these conditions. If we replace a_{1},a_{2},a_{3},a_{4} by 2a_{1},2a_{2},2a_{3},2a_{4} then the conditions will still be satisfied, but \sum_{r = 1}^{4} a_{r}|Z_{r}|^2 will be doubled.
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  3. #3
    Super Member fardeen_gen's Avatar
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    The problem set of the complex numbers section of my text seems to be full of wrong problems. This makes it two wrong problems in a day
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