Question

For a complex number written in polar form, it's representation is unique as long as the argument is restricted to [0, 2pi). True or False?

Answer 1

The more standard restriction is usually -pi to pi.
But as long as it's only one full rotation then it should be true.
I don't think there is any trickery in this question .. yah seems like it's true :3

Example:\[\Large\rm z_1=e^{i \frac{\pi}{2}}\]\[\Large\rm z_2=e^{i\frac{5\pi}{2}}\]
z1 and z2 do NOT have unique representation. z2 spins an extra time around and lands in the same place as z1, yah? :)

Answer 2

In the example I was trying to show what happens when we DO NOT restrict the angle, just so that's clear.