Question

Are $\mathbb{R}[X] / (X^2 +1)$ and $\mathbb{C}$ homeomorphic?

score 361 · Answer 1 · 2026-03-25 08:07:39

361

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Are $\mathbb{R}[X] / (X^2 +1)$ and $\mathbb{C}$ homeomorphic?

Published on 25 Mar 2026 - 8:07

score 1.5k · Answer 2 · 2026-03-23 10:25:25

1.5k

Views

Cube root of numbers such as $2+11i$

Published on 23 Mar 2026 - 10:25

score 86 · Answer 3 · 2018-06-30 09:46:48

86

Views

Solve $a z - b \bar{z}^2 - c z^2 \bar{z} = 0$

Published on 30 Jun 2018 - 9:46

score 193 · Answer 4 · 2018-06-30 11:15:20

193

Views

Let $f$ be holomorphic on $\mathbb{D}=\{z\in\mathbb{C} | |z|\leq 1\}$. Prove the following.

Published on 30 Jun 2018 - 11:15

score 434 · Answer 5 · 2018-06-30 19:39:44

434

Views

Complex number rotation - Wildberger approach

Published on 30 Jun 2018 - 19:39

score 788 · Answer 6 · 2026-03-24 19:48:41

788

Views

Infinite Knight's Tour

Published on 24 Mar 2026 - 19:48

score 119 · Answer 7 · 2018-07-01 18:07:03

119

Views

maximum modulus principle; function bounded

Published on 01 Jul 2018 - 18:07

score 31 · Answer 8 · 2018-07-01 21:43:18

31

Views

Why is it true that $\sum_{k=1}^{m-1} e(jk/m) = 0$ if $m$ does not divide $j$; and $m$ if $m$ does divide $j$?

Published on 01 Jul 2018 - 21:43

score 24 · Answer 9 · 2018-07-01 22:13:18

Rewrite $\left\vert\sum_{k\in B} \exp\left(\frac{2\pi ijk}{p} \right)\right\vert^2$, where $p$ is a prime $\ge 3$ and $B \subset \{1,2,...,p-1\}$.

score 1k · Answer 10 · 2026-03-25 12:38:10

1k

Views

Argument range for branch cut of $[-1,1]$?

Published on 25 Mar 2026 - 12:38

score 375 · Answer 11 · 2018-07-01 23:29:31

375

Views

Express the following as a finite sum of complex exponentials

Published on 01 Jul 2018 - 23:29

score 726 · Answer 12 · 2018-07-02 10:11:20

726

Views

Express the following complex numbers in the form of $a+bi$

Published on 02 Jul 2018 - 10:11

score 846 · Answer 13 · 2026-03-26 01:51:16

846

Views

Use complex numbers to prove that the composition of rotations is another rotation

Published on 26 Mar 2026 - 1:51

score 37 · Answer 14 · 2018-07-02 14:48:20

37

Views

Simplification of complex exponentiation of a number

Published on 02 Jul 2018 - 14:48

score 55 · Answer 15 · 2018-07-02 18:37:37

55

Views

Show steps to convert $C^3-3CS^2$ to $4C^3-3C$

Published on 02 Jul 2018 - 18:37

List Question

Are $\mathbb{R}[X] / (X^2 +1)$ and $\mathbb{C}$ homeomorphic?

Cube root of numbers such as $2+11i$

Solve $a z - b \bar{z}^2 - c z^2 \bar{z} = 0$

Let $f$ be holomorphic on $\mathbb{D}=\{z\in\mathbb{C} | |z|\leq 1\}$. Prove the following.

Complex number rotation - Wildberger approach

Infinite Knight's Tour

maximum modulus principle; function bounded

Why is it true that $\sum_{k=1}^{m-1} e(jk/m) = 0$ if $m$ does not divide $j$; and $m$ if $m$ does divide $j$?

Rewrite $\left\vert\sum_{k\in B} \exp\left(\frac{2\pi ijk}{p} \right)\right\vert^2$, where $p$ is a prime $\ge 3$ and $B \subset \{1,2,...,p-1\}$.

Argument range for branch cut of $[-1,1]$?

Express the following as a finite sum of complex exponentials

Express the following complex numbers in the form of $a+bi$

Use complex numbers to prove that the composition of rotations is another rotation

Simplification of complex exponentiation of a number

Show steps to convert $C^3-3CS^2$ to $4C^3-3C$

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