how do we find out maximum value of $|f(z)|$:complex analysis
129343
What is the maximum value of $|f(z)|$ on the unit disc $D=\{z \in \mathbb C:|z|\leq 1\}$?
109943
Estimates of the value of a holomorphic function and its derivative
157911
Which value of $a$ maximizes $\int_{a-1}^{a+1}\frac{1}{1+x^{8}}dx$?
149544
maximum of monic polynomial on unit circle is 1 implies $p(z)=z^n$
23801
A reflection question about a complex function
146266
Find the maximum value of the expression ${\frac {x}{1+x^2}} + {\frac {y}{1+y^2}}+{\frac {z}{1+z^2}}$.
1366
Complex Analysis: Complex Integral
112597
Extreme point of unit balls, the complex case
14117
Holomorphic function has at most countably zeros
152274
An exercise from Conway's Complex Analysis on an application of Schwarz's Lemma
58924
Possible values of $\int \frac{dz}{\sqrt{1-z^2}}$ over a closed curve in a region?
154223
Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$
157328
A complex analysis problem to prove an inequality
149634
$ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
108846
Estimate of analytic function in a unit disk
118136
Finding univalent function with $f(z_1)=z_2$
29276
technique of proving continuity complex function