Paper 2, Section I, E

Further Complex Methods
Part II, 2013

(i) Find all branch points of (z31)1/4\left(z^{3}-1\right)^{1 / 4} on an extended complex plane.

(ii) Use a branch cut to evaluate the integral

22(4x2)1/2dx\int_{-2}^{2}\left(4-x^{2}\right)^{1 / 2} d x