Sketch the C1 paths a: [0; 1] -> C, t -> t + it2 and b: [0; 1 + i]. Then compute the following integrals.
∫Re(z)dz over a
∫Re(z)dz over b
The Attempt at a Solution
Sketching a seems ok, y axis is Imaginary, x axis is Real, and the path is a quadratic between 0 and 1.
However I'm not sure about b...
As for the integrals, is it just a case of integrating Re(a(t))a'(t)dt between 0 and 1, then integrating Re(a(t))a'(t)dt between 0 and 1+i?