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Complex numbers

  1. Jan 23, 2017 #1
    1. The problem statement, all variables and given/known data
    [tex]\frac{z-1}{z+1}=i [/tex]
    I found the cartesian form, z = i, but how do I turn it into polar form?


    3. The attempt at a solution
    [tex] |z|=\sqrt{0^2+1^2}=1[/tex]
    [tex]\theta=arctan\frac{b}{a}=arctan\frac{1}{0}[/tex]

    Is the solution then that is not possible to convert it to polar form?
     
  2. jcsd
  3. Jan 23, 2017 #2

    Math_QED

    User Avatar
    Homework Helper

    Notice that ##\tan(\frac{\pi}{2} + k \pi)## with ## k \in \mathbb{Z}## is not defined. Draw ## i ## in the complex plane. What can you conclude?
     
  4. Jan 23, 2017 #3

    Mark44

    Staff: Mentor

    What is the exact problem statement? Are you given that ##\frac{z-1}{z+1}=i##?

    Doing some work on this, it appears that if ##\frac{z-1}{z+1}=i##, then ##z = i##
    It would have been helpful to me for you to say what is given, and what you needed to do.
    It's easy to convert to polar form. What is |i|?
    What is the angle that i makes with the horizontal axis?
     
  5. Jan 23, 2017 #4
    [tex] 90\circ[/tex]? I felt it was clear
    |z| is the length
     
  6. Jan 23, 2017 #5

    Mark44

    Staff: Mentor

    The angle is ##\pi/2##, in radians, or 90°.
    The magnitude is NOT |z|. I asked what is the magnitude of i?

    No, it wasn't clear.

    Clear would be something like this:
     
  7. Jan 23, 2017 #6
    Ok, my bad. But thanks :)
     
  8. Jan 23, 2017 #7

    Mark44

    Staff: Mentor

    You're welcome!
     
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