weird properties of complex exponentials: $e^{i 2 \pi f(x)} = 1$
19628
What is wrong with this fake proof $e^i = 1$?
131424
which of the following is NOT a possible value of $(e^{f})''(0)$??
109900
Why is $e^{\pi \sqrt{163}}$ almost an integer?
56836
Intuitive explanation of Cauchy's Integral Formula in Complex Analysis
154411
How can I intuitively understand complex exponents?
7835
Tricky elementary integral $\int_{0}^{\frac{\pi}{2}}x\cot(x)dx$.
67588
Why does $|e^{ix}|^2 = 1$?
27347
Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
4833
Compute $\int_0^1\frac{f(x)}{f(x)+f(1-x)}dx$ and $\int_{-\pi}^{\pi}\frac{1}{1+e^{\sin (x)}}\,dx$?
150417
Two apparently different antiderivatives of $\frac{1}{2 x}$
138360
Exponents and absolute value w/ complex numbers
38751
What is the antiderivative of $e^{-x^2}$
109295
Proving $1-\exp(-4x^2/ \pi) \ge \text{erf}(x)^2$
91196
Complex Integration of $\int_0^\infty e^{-ax}\cos(bx)\,dx$
47845
Mirror algorithm for computing $\pi$ and $e$ - does it hint on some connection between them?
10070
Complex analysis: Calculating $\int_{-\infty}^{\infty} \frac{\sin x}{x} dx$ by using $f(z) = \frac{e^{iz} - 1}{iz}$
42745
Validity and Equivalence of two definitions of the real exponential function