Find out the condition for $k$ such that the locus of $z$ is a circle.
40824
Complex Equation Of a Circle $|z-z_1|^2+|z-z_2|^2=k$.
118501
Proving the length of a circle's arc is proportional to the size of the angle
117781
Proving that $S=\{\frac{1}{n}:n\in\mathbb{Z}\}\cup\{0\}$ is compact using the open cover definition
73419
For $f$ entire and $\{f(kz) : k \in \mathbb{C}\}$ a normal family, prove that $f$ is a polynomial.
115677
Prove the equality of circle's areas
94962
For complex $z$, $|z| = 1 \implies \text{Re}\left(\frac{1-z}{1+z}\right)  = 0$
147429
Set of points in $\mathbb{C}$ s.t. $z^{n-1} = \overline z$
158235
Laurent Series for $\cot(\pi z)$
149451
For what $n$ does a hyperbolic regular $n$-gon exist around a circle?
140968
Proof for Property of Complex Numbers
126989
Prove that $g(z)=\overline{f(z)}$ is complex diﬀerentiable at $a$ if and only if $f'(a) = 0$.
71074
The locus of the intersection point of two perpendicular tangents to a given ellipse
85869
Four complex numbers $z_1,z_2,z_3,z_4$ lie on a generalized circle if and only if they have a real cross ratio $[z_1,z_2,z_3,z_4]\in\mathbb{R}$
63447
Prove that the kernel of a homomorphism is a principal ideal. (Artin, Exercise 9.13)
61262
Is $\cot(z)-\frac1z$ bounded on a given circle?
142530
Let K be a field, and $I=(XY,(X-Y)Z)⊆K[X,Y,Z]$. Prove that $√I=(XY,XZ,YZ)$.
139168
Prove that there is an unique $z$ s.t. $f(z) = z$ where $z$ is a complex number