A friend of mine and I were re-visiting Euler’s identity: \(e^{ \pm i\theta } = \cos \theta \pm i\sin \theta\) and we started looking at spirals of the form: \((e^z)^n = [r (\cos \theta \pm i\sin \theta)]^n\) where \(\theta\) and \(r\) are fixed while n varies from \((-\infty, \infty)\)