$ z = 1 + 2i $ - Prove that $ z^n \notin \mathbb{R} $
34252
$ z^n = a_n + b_ni $ Show that $ b_{n+2} - 2b_{n+1} + 5b_n = 0 $ (complex numbers)
52800
Show that $z^5-1=(z-1)(z^2+2z\cos{\pi \over 5}+1)(z^2-2z\cos{2\pi \over 5}+1)$
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
52178
Prove the roots of $z^7+7z^4+4z+1=0$ lie inside a circle of radius $2$.
79808
Prove the representation of complex numbers is parallelogram
137285
Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
139168
Prove that there is an unique $z$ s.t. $f(z) = z$ where $z$ is a complex number
7105
Prove that $\prod\limits_{i=1}^n \frac{2i-1}{2i} \leq \frac{1}{\sqrt{3n+1}}$ for all $n \in \Bbb Z_+$
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
112933
Show that $Z\times Z$ is not cyclic...
55266
Prove that $(n+1)^{n-1}<n^n$
102553
How to show that $f(z) = f(i)$
54370
If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
51314
How to prove that a complex number is not a root of unity?
12020
Prove $\sqrt{n+1}-\sqrt{n}\lt \frac{1}{2\sqrt{n}}$