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Doubt about condition solutions of complex line equation

  1. Dec 10, 2014 #1
    Dear All,
    Please help me clear some doubts about Theorem 3.3.1 in the 1st attachment.
    The condition ## |a| = |b| ## has only 8 cases right? ## { x+iy. x - iy, -x + iy, -x - iy, y + ix, y - ix, -y + ix, -y - ix } ##

    so for the condition ## |a| = |b| ## and ## b \bar c = \bar a c ## in (2) and (3) in the attachement, what must ##b## and ##\bar a## be for them to to satisfy this equation given that C is a complex number of the form ## Cx + iCy ##.

    why is there a line of solutions in (3)? usually you only get one imaginary and one real value for z right??

    In the 2nd attachement, I have tried to do question 3. what does in the direction of b mean? does it pass through b also?? c =0 right? can you please give examples of the complex number b?


    Attached Files:

    Last edited: Dec 10, 2014
  2. jcsd
  3. Dec 11, 2014 #2


    Staff: Mentor

    No, and how are x + iy, x - iy, etc. conditions? These are complex numbers. I don't see that they are conditions in any way. For example, consider a = 0 + 1i and b = -1/2 + (√3/2)i. These two complex numbers have the same magnitude, but I don't see how they are included in your eight cases, whatever it is you mean by them.

    b is a complex number, so you can think of it as being a vector, with its tail at the origin and its head at the point in the complex point (b1, b2). What direction does it point?
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