For which values of c is the topological space xc : = {(x, y) € c^2 e: x^2 - y^2 = c} a riemann surface? you do not need to explicitly construct charts, but you do need to prove your answer is correct. (warning: use the implicit function theorem to produce a complex structure. the hardest part is proving that x. is not a manifold for certain values of c. if you get stuck, try drawing a picture.)

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: multiply exponents per exponent rules to get: remember you subtract exponents from the denominator and add exponents in the numerator so: simplify further: so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.

The answer might be a