# Imaginary numbers

1. Apr 18, 2007

### trajan22

w=8i
I need to put this in polar form but how can i do this since this would be
w=8(cos(theta)+isin(theta))
I cant find the angles because tan(theta)=8/0
which of course is undefined. Is there something that I am doing wrong?

2. Apr 18, 2007

### cepheid

Staff Emeritus
Nope. You haven't done anything wrong. tan(theta) simply isn't defined for certain angles. Which ones? The good news is that you can draw a picture and see immediately what the angle is. Hint, a "vector" to this point in the complex plane would lie completely along the imaginary axis. So what would theta be?

3. Apr 19, 2007

### trajan22

So it could be either pi/2, or 2pi/3 but considering that 8 is a positive number then the angle must be pi/2 right?

4. Apr 19, 2007

### Vagrant

Why don't you just substitute pi/2 in w=8[cos(theta)+isin(theta)] and see which one gives you the correct ans?

5. Apr 19, 2007

### cristo

Staff Emeritus
I think you mean it can be pi/2 or 3pi/2. You are correct that it must be pi/2. One way to see this is to plot the point on the argand diagram. 8i lies on the positive imaginary axis, and so the principal argument is the angle between the positive real axis and the positive imaginary axis, measured anticlockwise; this is equal to pi/2.