Question

$a_i$ are the n-th roots of $1\in\mathbb{C}$, why does $(1-a_2)\cdot...\cdot(1-a_n)=n$?

score 51 · Answer 1 · 2026-03-26 11:18:09

51

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$a_i$ are the n-th roots of $1\in\mathbb{C}$, why does $(1-a_2)\cdot...\cdot(1-a_n)=n$?

Published on 26 Mar 2026 - 11:18

score 224 · Answer 2 · 2026-03-25 17:18:38

224

Views

A rotating polygonal line with increasing side length cannot end up where it started!

Published on 25 Mar 2026 - 17:18

score 194 · Answer 3 · 2019-03-21 07:18:38

194

Views

If $z=re^{i\theta}$, how do I prove that $|e^{iz}| = e^{-r \sin(\theta)}$?

Published on 21 Mar 2019 - 7:18

score 383 · Answer 4 · 2026-04-04 07:25:09

383

Views

argument of log (z) for different branches

Published on 04 Apr 2026 - 7:25

score 105 · Answer 5 · 2026-03-29 04:44:04

105

Views

Least value of $\left|2017 z+\frac{1}{2018z}\right|$ for complex $z$ with $|z|\geq 2019$

Published on 29 Mar 2026 - 4:44

score 169 · Answer 6 · 2026-03-26 09:58:12

169

Views

Direct product decomposition of the group of complex roots of unity

Published on 26 Mar 2026 - 9:58

score 46 · Answer 7 · 2019-03-22 17:17:14

46

Views

If $a_n\rightarrow a$ then $|a_n|\rightarrow |a|$ why does it not work for series?

Published on 22 Mar 2019 - 17:17

score 256 · Answer 8 · 2026-03-26 09:49:31

256

Views

Another Roots of Unity Sum

Published on 26 Mar 2026 - 9:49

score 59 · Answer 9 · 2026-03-25 17:26:26

59

Views

Understanding entire functions

Published on 25 Mar 2026 - 17:26

score 84 · Answer 10 · 2026-03-29 06:29:07

84

Views

Finding the roots of a complex number

Published on 29 Mar 2026 - 6:29

score 32 · Answer 11 · 2019-03-23 16:46:22

32

Views

Calculating the given power of a complex number

Published on 23 Mar 2019 - 16:46

score 396 · Answer 12 · 2026-03-25 10:56:03

396

Views

Finding the Möbius transformation from the unit disk to the half plane $\{Re(z)\geq3\}$

Published on 25 Mar 2026 - 10:56

score 633 · Answer 13 · 2019-03-23 22:39:02

633

Views

Prove that if $|z+w|=|z-w|$ then $z\overline{w}$ is purely imaginary.

Published on 23 Mar 2019 - 22:39

score 70 · Answer 14 · 2019-03-24 00:51:46

70

Views

Why do $x^2+y^2=\left(3+2i\right)^2$ and $x^2+y^2=25$ give the same circle?

Published on 24 Mar 2019 - 0:51

score 352 · Answer 15 · 2026-03-25 17:18:20

352

Views

Understanding infinite products convergence

Published on 25 Mar 2026 - 17:18

List Question

$a_i$ are the n-th roots of $1\in\mathbb{C}$, why does $(1-a_2)\cdot...\cdot(1-a_n)=n$?

A rotating polygonal line with increasing side length cannot end up where it started!

If $z=re^{i\theta}$, how do I prove that $|e^{iz}| = e^{-r \sin(\theta)}$?

argument of log (z) for different branches

Least value of $\left|2017 z+\frac{1}{2018z}\right|$ for complex $z$ with $|z|\geq 2019$

Direct product decomposition of the group of complex roots of unity

If $a_n\rightarrow a$ then $|a_n|\rightarrow |a|$ why does it not work for series?

Another Roots of Unity Sum

Understanding entire functions

Finding the roots of a complex number

Calculating the given power of a complex number

Finding the Möbius transformation from the unit disk to the half plane $\{Re(z)\geq3\}$

Prove that if $|z+w|=|z-w|$ then $z\overline{w}$ is purely imaginary.

Why do $x^2+y^2=\left(3+2i\right)^2$ and $x^2+y^2=25$ give the same circle?

Understanding infinite products convergence

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