Integration in complex plane, circle proof
18836
Complex integral over a circle
30829
A question in Complex Analysis $\int_0^{2\pi}\log(1-2r\cos x +r^2)\,dx$
84267
Real integral by keyhole contour
115677
Prove the equality of circle's areas
59123
Mapping circles via inversion in the complex plane
69020
Complex analysis : If $z =re^{i\theta}$, then prove that $|e^{iz}| =e^{-r\sin\theta}$
1516
How did you prove this integral?
84826
Evaluating $\int_0^{2 \pi} e^{\cos x} \cos (nx - \sin x) \,dx$ using complex analysis
157200
Roots of a equation on a complex plane
17566
line integral (multivariable calculus)
142299
Proving theorem connecting the inverse of a holomorphic function to a contour integral of the function.
16582
Show that $n$ lines separate the plane into $\frac{n^2+n+2}{2}$ regions
88769
Image of complex circle under polynomial
61585
Why is area of a surface of revolution integral $2\pi y~ds$? not '$dx$'?
89601
Rusty at complex integrals, finding error in steps
67186
Complex analysis integration question
47779
Why does this integral have a complex component?