question archive Using the function f(z) = (z*)^2 in parts (a,b) and the function f(z) = z^2 in (c,d)
Using the function f(z) = (z*)^2 in parts (a,b) and the function f(z) = z^2 in (c,d)
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Using the function f(z) = (z*)^2 in parts (a,b) and the function f(z) = z^2 in (c,d).
In this question we are going to integrate two complex functions from the point 0 to 1 +i along two different paths. One path L is the diagonal line segment, which we can parametrize as Z(t) = (1 + i)t for t = 0 to 1. The other path C is the parabola Z(t) = t 2 + it for t = 0 to 1. (
a,b)Calculate R L f(z)dz and R C f(z)dz where f(x + iy) = x − iy. I don't mind telling you to expect different answers.
(c) If we use f(x + iy) = x + iy, i.e. f(z) = z^2, we would expect the integrals along L, C to be the same. Why?
(d)Use the Fundamental Theorem of Calculus to calculate R 1+i 0 zdz.
