The discussion revolves around converting a complex number, specifically derived from the equation \(\frac{z-1}{z+1}=i\), into polar form after finding its Cartesian representation as \(z = i\). The subject area involves complex numbers and their representations in different forms.
There is an ongoing exploration of how to express the complex number in polar form, with some participants providing guidance on identifying the magnitude and angle. Multiple interpretations of the problem statement are being discussed, and there is no explicit consensus on the clarity of the initial question.
Participants note the importance of clearly stating the problem and the assumptions involved, as well as the potential confusion regarding the definitions of magnitude and angle in the context of polar coordinates.
mr-feeno said:Homework Statement
\frac{z-1}{z+1}=i
I found the cartesian form, z = i, but how do I turn it into polar form?The Attempt at a Solution
|z|=\sqrt{0^2+1^2}=1
\theta=arctan\frac{b}{a}=arctan\frac{1}{0}
Is the solution then that is not possible to convert it to polar form?
What is the exact problem statement? Are you given that ##\frac{z-1}{z+1}=i##?mr-feeno said:Homework Statement
\frac{z-1}{z+1}=i
I found the cartesian form, z = i, but how do I turn it into polar form?
It's easy to convert to polar form. What is |i|?mr-feeno said:The Attempt at a Solution
|z|=\sqrt{0^2+1^2}=1
\theta=arctan\frac{b}{a}=arctan\frac{1}{0}
Is the solution then that is not possible to convert it to polar form?
90\circ? I felt it was clearMark44 said: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?
mr-feeno said:90\circ? I felt it was clear
|z| is the length
If ##\frac{z - 1}{z + 1} = i##, solve for z, writing it in polar form.
Mark44 said: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:
You're welcome!mr-feeno said:Ok, my bad. But thanks :)