Can I say that $1^{\frac{1}{2}} = (e^{2i\pi})^{\frac{1}{2}} =e^{i\pi} = -1 $?
11089
For which complex $a,\,b,\,c$ does $(a^b)^c=a^{bc}$ hold?
5679
Why is $2\pi i \neq 0?$
70974
How can zero divided by $i$ be $2\pi$?
49444
Why isn't $e^{2\pi xi}=1$ true for all $x$?
140459
Why is $\left(e^{2\pi i}\right)^i \neq e^{-2 \pi}$?
113334
If $x+\frac{1}{x}=\frac{1+\sqrt{5}}{2}$ then $x^{2000}+\frac{1}{x^{2000}}= $?
10068
$f(x,y)= e^{-\frac{1}{x^2+y^2}}$ when $(x,y)\neq (0,0)$ and $f(0,0)=0$.
82391
Why does $\sum_{k=1}^{\infty}\frac{{\sin(k)}}{k}={\frac{\pi-1}{2}}$?
114734
Prove that $\frac{1}{2\pi i}\int_\mathcal{C} |1+z+z^2+\cdots+z^{2n}|^2~dz =2n$ where $\mathcal{C}$ is the unit circle
124209
How is $\ln(-1) = i\pi$?
109674
If $(I-T)^{-1}$ exists, can it always be written in a series representation?
81875
why is $\sqrt{-1} = i$ and not $\pm i$?
11059
Verify the identity: $\tan^{-1} x +\tan^{-1} (1/x) = \pi /2$
85311
Proving that $e^{\pi}-{\pi}^e\lt 1$ without using a calculator
80710
Does $\int_{-1}^1 \frac 1 x dx$ equal zero?
47166
Is there a function whose inverse is exactly the reciprocal of the function, that is $f^{-1} = \frac{1}{f}$?
158627
$e^{\left(\pi^{(e^\pi)}\right)}\;$ or $\;\pi^{\left(e^{(\pi^e)}\right)}$. Which one is greater than the other?