In functions with complex arguments it's been said that to determine whether a point is a branch point or not we have to travel around that point and see if we get the same answer. How do I travel around a point? How can I find the branch points of the function $\sqrt{x^2-4}$. I know $2 -2$ and $\infty$ are possible branch points but how do I test them?
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Example 1.4 at the following link is pretty close to what you want. It's for $\sqrt{x^2-1}$ https://people.maths.bris.ac.uk/~maavm/mathmethods_files/branch_cuts.pdf – Martin Hansen Nov 20 '20 at 20:15
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could you help me go through the solution please. – Erinç Utku Öztürk Nov 21 '20 at 15:26
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There's an explanation for $\sqrt{x^2+1}$ here : https://math.stackexchange.com/questions/988828/how-to-find-the-branch-points-and-cut Can you adapt it for your case ? – Martin Hansen Nov 21 '20 at 18:47
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There's some nice visualisations here : https://mathematica.stackexchange.com/questions/123977/branch-cut-of-sqrtx2-1 – Martin Hansen Nov 22 '20 at 07:48
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1understood, thank you for your answers! – Erinç Utku Öztürk Nov 22 '20 at 12:37