# Complex numbers

## 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?

member 587159

## 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?

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?

Mark44
Mentor

## Homework Statement

$$\frac{z-1}{z+1}=i$$
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

$$|z|=\sqrt{0^2+1^2}=1$$
$$\theta=arctan\frac{b}{a}=arctan\frac{1}{0}$$

Is the solution then that is not possible to convert it to polar form?
It's easy to convert to polar form. What is |i|?
What is the angle that i makes with the horizontal axis?

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?
$$90\circ$$? I felt it was clear
|z| is the length

Mark44
Mentor
$$90\circ$$? 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.

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 :)

Mark44
Mentor
Ok, my bad. But thanks :)
You're welcome!