If $|z+w|=|z-w|$, prove that $\arg z-\arg w =\pm\pi/2$
48038
If $z$ and $w$ are complex numbers such that $|(z+w)| = |(z-w)|$, prove that $\arg(z)-\arg(w) = \pm (\pi/2)$
46353
Proof that $\cos(\pi/3)=1/2$
148178
What points in the complex plane satisfy $|z|=arg(z)$.
99676
Prove $\sum{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$
64096
Prove that $||z_1|-|z_2|| \leq |z_1-z_2|$.
3109
Prove that $(p+q)^m \leq p^m+q^m$
114217
What is the value of $\operatorname{Arg}(\frac{z}{\bar{z}})$?
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
19216
Proving that $\arctan(x)+\arctan(1/x)=\pm \pi/2$, could this line of reasoning possibly be correct?
79808
Prove the representation of complex numbers is parallelogram
25967
Prove $\csc(x)=\sum_{k=-\infty}^{\infty}\frac{(-1)^k}{x+k\pi}$
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
21737
If $A|B$ and $B|A$ then prove $A=\pm B$
114734
Prove that $\frac{1}{2\pi i}\int_\mathcal{C} |1+z+z^2+\cdots+z^{2n}|^2~dz =2n$ where $\mathcal{C}$ is the unit circle
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
50266
In the following figure prove that: $AK||BC$