Let $z_1,z_2,z_3 \in \mathbb{C}$ with $z_i=1$ for $i=1,2,3$ and $z_1+z_2+z_3$. Show that $z_i$ are vertices for a equilateral triangle.
103172
showing certain vertices form an equilateral triangle
5297
If G is a finite abelian group and $a_1,...,a_n$ are all its elements, show that $x=a_1a_2a_3...a_n$must satisfy $x^2=e$.
52800
Show that $z^5-1=(z-1)(z^2+2z\cos{\pi \over 5}+1)(z^2-2z\cos{2\pi \over 5}+1)$
102320
Is my solution correct for solving $\cos(z)=2$, $z\in \mathbb{C}$
112740
Prove the triangle is equilateral given that a quadrilateral related to its circumcircle is a kite
131919
Vertices of equilateral triangle inscribed in the unit circle
110723
Catalan numbers and triangulation
129935
Coloring problem with equilateral triangles
130109
Equilateral Triangle from three complex points
55975
Let $a$, $b$ and $c$ be the three sides of a triangle. Show that $\frac{a}{b+c-a}+\frac{b}{c+a-b} + \frac{c}{a+b-c}\geqslant3$.
89493
Prove that circumcentre of $ABH,BCH,CAH$ are the vertices of a triangle congruent to $ABC$
92916
Show that $(2,0,4) , (4,1,-1) , (6,7,7)$ form a right triangle
156596
Prove $r^2+r_1^2+r_2^2+r_3^2=16R^2-a^2-b^2-c^2$ for a triangle with sides $a$, $b$, $c$, circumradius $R$, inradius $r$, exradii $r_1$, $r_2$, $r_3$
94091
In $ \triangle ABC$ show that $ 1 \lt \cos A + \cos B + \cos C \le \frac 32$
12158
Show that $\arctan\frac{1}{2}+\arctan\frac{1}{3}=\frac{\pi}{4}$
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
88956
For any three vectors $x,y,z\in\mathbb{R}^d$, we have $ \|y-z\|\cdot\|x\|\leq\|x-y\|\cdot\|z\|+\|z-x\|\cdot\|y\|$