If $z_1+z_2+z_3=0$ and $|z_1|=|z_2|=|z_3|=1$, then $z_1,z_2,z_3$ are the vertices of an equilateral triangle.
131919
Vertices of equilateral triangle inscribed in the unit circle
143281
How to solve $z^2-(1-3i)z-2i-2=0$
40596
Proving a relation between inradius ,circumradius and exradii in a triangle
109288
Prove that $x^3+y^3+z^3-3xyz=1$ defines a surface of revolution
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
34393
Variation of Pythagorean triplets: $x^2+y^2 = z^3$
40447
Let $A = \mathbb{Z}$, $B = [−1, \pi]$, $C = (2, 7)$. List all elements of $A \cap (B^c \cap C)$.
152643
$(xy + 1)(yz + 1)(zx + 1) $ is a perfect square if and only if each factor is
74977
When does $az + b\bar{z} + c = 0$ represent a line?
93170
Find the side of an equilateral triangle given only the distance of an arbitrary point to its vertices
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
115929
In a triangle $\angle A = 2\angle B$ iff $a^2 = b(b+c)$
27062
Given complex $|z_{1}| = 2\;\;,|z_{2}| = 3\;\;, |z_{3}| = 4\;\;$ : when and what is $\max$ of $|z_{1}-z_{2}|^2+|z_{2}-z_{3}|^2+|z_{3}-z_{1}|^2$
132081
Geometrical interpretation of $(\sum_{k=1}^n k)^2=\sum_{k=1}^n k^3$
22241
Do there exist an infinite number of 'rational' points in the equilateral triangle $ABC$?
117001
Find all solutions for $z^3 = \overline{z}$
130109
Equilateral Triangle from three complex points