# Complex Integrals

## Homework Statement

integral(e^(iz)dz) with bounds from pi to i.
I need to evaluate using : along the straight line joining the limits, along segments of the coordinate axes joining the limits, and estimate using integral <= L*M and compare the estimates with the values.

I am totally confused on how to do this. Do I convert z to x+iy and do the bounds change?

I have another integral with z conjugate about the unit circle. I think I have an idea on this one on converting to x-iy and seeing that this will equal 2ipi.

I am also asked to evaluate this same integral taken in the positive sense about the square with x=+-1, y=+-1. I know this involves 4 segments, but my problem is finding this 4 segments. I know the answer is 8i, but how to get there?

Related Calculus and Beyond Homework Help News on Phys.org
You can parametrize the path from pi to i, e.g by taking:

z(t) = pi + (i-pi)t

The starting point is then at t = 0 and the end point at t = 1.

integral f(z)dz along the path then means:

f(z(t))d(z(t)) from t = 0 to t = 1.

We have dz = (i-pi) dt

and

f(z(t)) = exp[i pi - (i pi + 1)t] = -exp[-(i pi + 1)t]

That makes a lot of sense actually.