- #1
indigogirl
- 9
- 0
I want to show that the integral from -1 to 1 of z^i = (1-i)(1+exp(-pi)/2
where the path of integration is any contour from z=-1 to z=1 that lies above the real axis (except for its endpoints).
So, I know that z^i=exp(i log(z)) and the problem states that |z|>0, and arg(z) is between -pi/2 and 3pi/2. But we didn't study how to integrate z^(complex number) in class, and I"m really confused on how to do this.
So, how do I integrate this?
where the path of integration is any contour from z=-1 to z=1 that lies above the real axis (except for its endpoints).
So, I know that z^i=exp(i log(z)) and the problem states that |z|>0, and arg(z) is between -pi/2 and 3pi/2. But we didn't study how to integrate z^(complex number) in class, and I"m really confused on how to do this.
So, how do I integrate this?