Argand Diagram

  • Thread starter Solidmozza
  • Start date
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.
Thanks.
 

HallsofIvy

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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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