Understanding branch cuts: f(z) = (a²-z²)^½

Gaining some understanding and intuition about branch points and branch cuts, taking as an example the function f(z) = (a²-z²)^½. We discuss how branch cuts can be used to make f(z) single-valued and show how making a branch cut is equivalent to restricting the arguments of z relative to the function's branch points. Next time we'll use these results to help evaluate a certain contour integral! About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard. Support the channel: https://ko-fi.com/benyelverton My website: https://benyelverton.com/ #mathematics #complexnumbers #branchpoints #branchcuts #exponential #complexanalysis #fractionalpowers #multivalued #argument #modulus #argganddiagram #maths #math #science #education