Complex numbers

  • Thread starter mr-feeno
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  • #1
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Homework Statement


[tex]\frac{z-1}{z+1}=i [/tex]
I found the cartesian form, z = i, but how do I turn it into polar form?


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?
 

Answers and Replies

  • #2
member 587159

Homework Statement


[tex]\frac{z-1}{z+1}=i [/tex]
I found the cartesian form, z = i, but how do I turn it into polar form?


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?

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?
 
  • #3
35,287
7,140

Homework Statement


[tex]\frac{z-1}{z+1}=i [/tex]
I found the cartesian form, z = i, but how do I turn it into polar form?
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.
mr-feeno said:

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?
It's easy to convert to polar form. What is |i|?
What is the angle that i makes with the horizontal axis?
 
  • #4
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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?
[tex] 90\circ[/tex]? I felt it was clear
|z| is the length
 
  • #5
35,287
7,140
[tex] 90\circ[/tex]? I felt it was clear
|z| is the length

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:
If ##\frac{z - 1}{z + 1} = i##, solve for z, writing it in polar form.
 
  • #6
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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:

Ok, my bad. But thanks :)
 
  • #7
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