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

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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.

#mathematics #complexnumbers #branchpoints #branchcuts #exponential #complexanalysis #fractionalpowers #multivalued #argument #modulus #argganddiagram #maths #math #science #education
  1. Dr Ben Yelverton
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Finally...something regarding complex analysis...love the video....I would greatly appreciate it if you would make more videos on this topic...especially branch cuts of more complicated functions....

DihinAmarasigha-uphf