If $z_1,z_2,z_3 \in \mathbb{C}$ and $|z_1|=|z_2|=|z_3|$ and $z_1+z_2+z_3=0$. Prove that $z_1,z_2,z_3$ are points of a equilateral triangle
103172
showing certain vertices form an equilateral triangle
109133
$a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$
86197
Let $z_1 = x_1 +iy_1 $ and $z_2 = x_2 +iy_2$ be two complex numbers. The dot product of $z_1$ and $z_2$ is defined by $ = x_1x_2+y_1y_2$
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 $[z_1,z_2,z_3,z_4]\in\mathbb{R}$
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
102175
$Z=XY$, $E_Z[Z]$, $E_{X,Y}[XY]$
89493
Prove that circumcentre of $ABH,BCH,CAH$ are the vertices of a triangle congruent to $ABC$
144769
Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$
101448
Is $\sin^2(z) + \cos^2(z)=1$ still true for $z \in \Bbb{C}$?
141816
factor $z^7-1$ into linear and quadratic factors and prove that $ \cos(\pi/7) \cdot\cos(2\pi/7) \cdot\cos(3\pi/7)=1/8$
135365
If $x, y, z$ are the side lengths of a triangle, prove that $x^2 + y^2 + z^2 < 2(xy + yz + xz)$
131919
Vertices of equilateral triangle inscribed in the unit circle
50417
Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.
37744
Prove that given $a,b,c > 0$, it is possible to construct a triangle with sides of length $a,b,c$ if and only if $pa^2+qb^2 > pqc^2$
140299
Inequality based on triangle: $\frac{3}{2}\le\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$
89838
Prove that $3 \le a+b+c \le 2\sqrt{3}$ in a triangle
22241
Do there exist an infinite number of 'rational' points in the equilateral triangle $ABC$?