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Argand Diagram

  1. Nov 1, 2005 #1
    Hi everybody!
    Could somebody please assist me with an explanation as to why the following: arg (z+3-2i) = 135degrees : has its centre at -3,2 and that is the place where you begin the argument (ie go 135 degrees)
    Please note, just beginning complex numbers. Sorry if cant understand question.
  2. jcsd
  3. Nov 1, 2005 #2


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    It would be nice to tell us exactly what you are trying to find! I.e. what do you go 135 degrees to?

    The statement that "arg(z+ 3- 2i)= 135 degrees" means that the line from the number z+3- 2i to the origin (0) makes a 135 degree angle with the real axis. I imagine the problem asks you to determine possible values for z.
    Write z+ 3- 2i as z- (-3+ 2i). The complex number -3+ 2i is represented on the Argand diagram by the point (-3, 2). We can think of z- (-3+2i) as a vector with its tail at (-3, 2) and its point at z. Now, starting from a horizontal line (parallel to the real axis), sweep 135 degrees counter clockwise (that gets you to the "upper left" quadrant, 45 degrees from either axis). z could be any point on that line. If this line were through (0,0) on an xy- plane, it would be the line y= -x: slope -1. Since it must go through (-3, 2), it has equation y= -(x+3)+ 2= -x- 1: z = x+(-x-1)i for x any real number.
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