6 problems.
- \(\int_0^\infty\frac{x^{a-1}}{1+x^n}\,dx=\frac{\pi}{n\sin\frac{a\pi}{n}}\) for \(0<a<n\)
- \(z_1,z_2,z_3\) form an equilateral triangle iff \(z_1^2+z_2^2+z_3^2=z_1z_2+z_2z_3+z_3z_1\)
- Cauchy integral of \(f\) on a simple closed curve, equal to \(A\) inside and \(-f(z)+A\) outside, when \(\lim_{z\to\infty}f(z)=A\)
- Entire univalent functions are affine/linear
- Conformal map from a lune to the unit disk
- A holomorphic map is a local bijection iff \(f'\neq 0\)