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

False

Answer 2

counter-example:
\[1+i = \sqrt{2}(\cos \frac{\pi}{4} +i \sin \frac{\pi}{4})\]
\[1+i = -\sqrt{2}(\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4})\]

Answer 3

see why this would be interesting to the mathematicians here!LOL