Recent content by ridethespiral

Hmm, I'm not really sure how to use the logarithm. Is it because if you take the principal logarithm, there will be a discontinuity in the principal argument going from -π to π? So if you take the logarithm defined on \mathbb{C} \backslash {(-\pi, \pi]} then the set isn't open. Or perhaps...

Homework Statement (i) Let U and V be open subsets of C with a function f defined on U \cup V suppose that both restrictions, f_u \mathrm{and} f_v are continuous. Show that f is continuous. (ii) Illustrate by a specific example that this may not hold if one of the sets U, V is not open...

Alright, so z(z-1) will have two square roots, so will the answer just be two?

Homework Statement How many branches does the function f(z) = \sqrt{z(1-z)} have on the set \Omega = \mathbb{C} \backslash [0,1] Homework Equations The Attempt at a Solution Not really sure how to go about it at all. Our lecturer didn't say too much about branches but...