Prove that $\alpha=\beta=\gamma$ where $\alpha,\beta, \gamma$ are complex numbers.
59239
For non-zero real $x$, $y$, $z$ and complex $a$, $b$, $c$ with $|a|=|b|=|c|$, if $x+y+z=0=ax+by+cz$, then $a=b=c$
139667
Show that $f(z) = cg(z)$ is valid for two analytic functions $f$ and $g$ given a certain relationship between them
30770
Prove that $C\left(\bigcup_{\alpha\in I} A_\alpha\right)=\bigcap_{\alpha\in I}C\left(A_\alpha\right)$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
6100
Show that $\left|\frac{\alpha - \beta}{1-\bar{\alpha}\beta}\right| < 1$ when $|\alpha|,|\beta| < 1$
81775
Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$
65141
Simple proof Euler–Mascheroni $\gamma$ constant
145632
Proving $\frac{1}{\cos^2\alpha}<\frac{\tan\beta-\tan\alpha}{\beta-\alpha}<\frac{1}{\cos^2\beta}$
129605
$ 2g(z)=g(\frac{z}{2}) + g(\frac{z+1}{2})$
149661
For $n=pq$, show that there exist $\alpha, \beta \in Z_n^*$ such that $\alpha, \beta \notin (Z_n^*)^2$ and $\alpha \cdot \beta \notin (Z_n^*)^2$.
115176
Can we say that $\left(a+b\right)^{\alpha}>a^{\alpha}+b^{\alpha}$ for all $a,b>0$ and $\alpha>1$?
69082
Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$
147684
Prove that $\sin \theta=\frac{3 \sin \alpha+\sin^3 \alpha}{1+3\sin^2 \alpha}$ using given condition
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
24785
How prove this equation $\alpha=\aleph_{0}\alpha$
141391
how to find $\Gamma(n+3/2)$