Prove that if $Re(z)>0$ then $|z+\sqrt{z^2-1}| \ge 1$
128383
Complex Analysis - Bruce P . Palka - Ex: 4.12
46039
Prove that if $x \in R,$ then there exists $n \in Z$ satisfying $x \leq n < x+1$
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
57670
Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
110826
prove that : $ i = \sqrt {-1}\ $
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
51659
If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
86211
If $x+y+z \geq xyz$ Prove that $x^2 + y^2 + z^2 \geq xyz$.
41293
Prove the inequalities $|z_1 +z_2| \geq \frac{1}{2}(|z_1|+|z_2|)|\frac {z_1} {|z_1|} +\frac {z_2} {|z_2|}|$
146546
Proving for all integer $n \ge 2$, $\sqrt n < \frac{1}{\sqrt 1} + \frac{1}{\sqrt 2}+\frac{1}{\sqrt 3}+\cdots+\frac{1}{\sqrt n}$
132431
Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
16774
If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$.
89509
Suppose $z \neq -1$ is a complex number of norm 1. Prove that $(\frac{1+z}{|1+z|})^2 =z $
36507
If $x,y>0$ and $x^2+y^3\ge x^3+y^4$, prove that $x^3+y^3 \le 2$.