Using Rouche's Theorem to find the number of solutions of $f(z)=z$ in the open unit disc
139168
Prove that there is an unique $z$ s.t. $f(z) = z$ where $z$ is a complex number
63731
Can we characterize the Möbius transformations that maps the unit disk into itself?
115229
Find the zeros of $h(z)=z^6-5z^4+3z^2-1$ within the unit disc - Verification
28594
Number of integer solutions of the following equation
42713
Solutions to the equation $ze^{a-z}=1$
129343
What is the maximum value of $|f(z)|$ on the unit disc $D=\{z \in \mathbb C:|z|\leq 1\}$?
82567
Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
28148
Are there any simple ways to see that $e^z-z=0$ has infinitely many solutions?
79925
Infinitely many values of $x$ that satisfy the equations
87723
Show a holomorphic function on unit disc with with $|f'(z) - f'(0)| < |f'(0)|$ is injective
133212
$\int_C \frac{\log z}{z-z_0} dz$ - Cauchy theorem with $z_0$ outside the interior of $\gamma$
127436
Conformal Maps onto the Unit Disc in $\mathbb{C}$
150689
All the zeroes of $p(z)$ lie inside the unit disk
7466
How would I prove that if an integer $n>2$, then $\bar{z}=z^{n-1}$ has $n+1$ solutions
151732
Number of solutions of polynomials in a field
77990
How many solutions $X^{10} - I=0$ has in $M_2(\mathbb{R})$?
127169
Show that the zeros of $\sum_{k=1}^n kz^{k-1}$ are inside the unit disc