Explore the intricacies of complex analysis in this 35-minute lecture focusing on roots of unity and rational powers of complex numbers. Delve into the application of complex logarithms, Log(z), and exponentials to compute fractional and rational powers of complex numbers. Examine special cases such as the n-th roots of unity and the square root of i. Gain valuable insights from Steve Brunton, an expert in the field, as he guides you through these advanced mathematical concepts. For more information and resources, visit eigensteve.com or databookuw.com, or follow @eigensteve on Twitter.