Polar Form of Imaginary Number w=8i - Undefined Tan(theta)

[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 can't find the angles because tan(theta)=8/0
which of course is undefined. Is there something that I am doing wrong?

 

[cepheid]

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?

 

[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?

 

[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?

 

[cristo]

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?

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.