# Complex numbers

1. Jan 23, 2017

### mr-feeno

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

3. 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?

2. Jan 23, 2017

### Math_QED

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. Jan 23, 2017

### 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?

4. Jan 23, 2017

### mr-feeno

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

5. Jan 23, 2017

### 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:

6. Jan 23, 2017

### mr-feeno

Ok, my bad. But thanks :)

7. Jan 23, 2017

### Staff: Mentor

You're welcome!