Inequality concerning complex numbers and their modulus properties
17519
Let $z \in\Bbb{C}^{\times}$ such that $|z^3+\frac{1}{z^3}|\leq 2$. Prove that $|z+\frac{1}{z}|\leq 2$.
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
24221
Complex numbers - minimum value proof
96127
Maximum of $|\sin(z)|$ as $\{z: |z| \leq 1 \} $
41293
Prove the inequalities $|z_1 +z_2| \geq \frac{1}{2}(|z_1|+|z_2|)|\frac {z_1} {|z_1|} +\frac {z_2} {|z_2|}|$
40700
Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$
76013
Evaluating a sequence of complex numbers: $|z_n - z_m| < \frac1{1+ |n-m|}$
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
46701
Complex Number Proof Questions
20857
About the limit of the coefficient ratio for a power series over complex numbers
80826
To prove $\left|\frac{p_n(z)}{q_m(z)}\right|\leq \frac{M}{|z|^{m-n}}$ for some $M>0$
19078
Prove an interpolation inequality
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
122156
An inequality concerning three positive numbers
5430
Using Cauchy's integral theorem to prove a inequality
73987
Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$
16852
$|e^a-e^b| \leq |a-b|$ for complex numbers with non-positive real parts