Prove $z_1$, $z_2$ ,$z_3$ on complex plane are collinear iff $\frac{z_3-z_1}{z_2-z_1}\in\mathbb R$
62297
What can be said about complex numbers $z_1, z_2, z_3$ if $\frac{z_1 - z_3}{z_2 - z_3}$ is real?
144188
Prove that $\cos(z)$ and $\sin(z)$ are surjective over the complex numbers.
155165
Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
38396
If $AD$, $BE$, $CF$ are exterior bisectors then $D,E,F$ are collinear
157200
Roots of a equation on a complex plane
140977
Why $\bar{z_1}z_2+\bar{z_2}z_3+\bar{z_3}z_1 \in \mathbb R \iff z_1, z_2, z_3 \text{ are along the same line}$
150528
Pythagorean triples $(a,b,c)$ and divisibility of $a$ or $b$ by $3$.
16774
If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$.
44705
Prove that $\frac{1}{a^3(b+c)}+\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)}\ge \frac32$
143000
Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.
26501
Proof using complex numbers
127397
$z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $
79808
Prove the representation of complex numbers is parallelogram
139168
Prove that there is an unique $z$ s.t. $f(z) = z$ where $z$ is a complex number
46701
Complex Number Proof Questions
52800
Show that $z^5-1=(z-1)(z^2+2z\cos{\pi \over 5}+1)(z^2-2z\cos{2\pi \over 5}+1)$
11857
$A$ be a complex $3\times 3$ matrix such that $A^3=-I$