Question

$ z_1^k+\cdots +z_n^k=0$ for all $k$ implies $z_i=0$ for all $i$

score 119 · Answer 1 · 2026-04-16 10:19:02

119

Views

$ z_1^k+\cdots +z_n^k=0$ for all $k$ implies $z_i=0$ for all $i$

Published on 16 Apr 2026 - 10:19

score 54 · Answer 2 · 2026-04-10 19:09:00

54

Views

Extra solutions when multiplying by complex conjugate

Published on 10 Apr 2026 - 19:09

score 352 · Answer 3 · 2026-04-12 11:59:04

352

Views

Is there a useful notion of complex area?

Published on 12 Apr 2026 - 11:59

score 135 · Answer 4 · 2026-04-17 14:33:33

135

Views

Prove $\left(\frac{1+\cos2\theta+i\sin2\theta}{1+\cos2\theta-i\sin2\theta}\right)^n = \cos2n\theta+i\sin2n\theta$

Published on 17 Apr 2026 - 14:33

score 27 · Answer 5 · 2026-04-11 05:02:06

27

Views

Polarform Solution e function

Published on 11 Apr 2026 - 5:02

score 74 · Answer 6 · 2026-04-16 14:03:06

74

Views

Sum of Cosines is $-1$

Published on 16 Apr 2026 - 14:03

score 142 · Answer 7 · 2026-04-16 06:50:17

142

Views

simplify $\sqrt[3]{x \sqrt[3]{ x \sqrt[3]{x ...}} }$ -- if $x$ is negative?

Published on 16 Apr 2026 - 6:50

score 542 · Answer 8 · 2026-04-10 22:59:23

542

Views

Show that the following matrix is equal to 0, where $\omega$ is a complex cube root of unity.

Published on 10 Apr 2026 - 22:59

score 85 · Answer 9 · 2026-04-28 16:31:08

85

Views

Are there different products that turn $\,\Bbb R^2$ into a field?

Published on 28 Apr 2026 - 16:31

score 114 · Answer 10 · 2026-04-17 00:43:17

114

Views

Show that $x^3+3y^3+9z^3-9xyz=1$ has infinitely many integer solutions.

Published on 17 Apr 2026 - 0:43

score 639 · Answer 11 · 2026-04-11 06:14:20

639

Views

If $1, \omega, \omega^2$ are cube roots, show that $(2-\omega)(2-\omega^2)(2-\omega^{19})(2-\omega^{23})=49$

Published on 11 Apr 2026 - 6:14

score 668 · Answer 12 · 2026-04-15 21:53:32

668

Views

If $\alpha, \beta$ are roots of $x^2-3ax+a^2=0$, find the value(s) of $a$ if $\alpha^2+\beta^2=\frac{7}{4}$.

Published on 15 Apr 2026 - 21:53

score 161 · Answer 13 · 2026-03-26 01:27:30

161

Views

Möbius transformation from a unit disc to its complement

Published on 26 Mar 2026 - 1:27

score 125 · Answer 14 · 2026-04-16 11:55:12

125

Views

If $z = (1+\cos a) +i \sin a$ and $a ∈ (0,2π)$, Then find $arg(z)$

Published on 16 Apr 2026 - 11:55

score 225 · Answer 15 · 2026-04-13 19:32:11

225

Views

Rotate sine wave on complex plane

Published on 13 Apr 2026 - 19:32

List Question

$ z_1^k+\cdots +z_n^k=0$ for all $k$ implies $z_i=0$ for all $i$

Extra solutions when multiplying by complex conjugate

Is there a useful notion of complex area?

Prove $\left(\frac{1+\cos2\theta+i\sin2\theta}{1+\cos2\theta-i\sin2\theta}\right)^n = \cos2n\theta+i\sin2n\theta$

Polarform Solution e function

Sum of Cosines is $-1$

simplify $\sqrt[3]{x \sqrt[3]{ x \sqrt[3]{x ...}} }$ -- if $x$ is negative?

Show that the following matrix is equal to 0, where $\omega$ is a complex cube root of unity.

Are there different products that turn $\,\Bbb R^2$ into a field?

Show that $x^3+3y^3+9z^3-9xyz=1$ has infinitely many integer solutions.

If $1, \omega, \omega^2$ are cube roots, show that $(2-\omega)(2-\omega^2)(2-\omega^{19})(2-\omega^{23})=49$

If $\alpha, \beta$ are roots of $x^2-3ax+a^2=0$, find the value(s) of $a$ if $\alpha^2+\beta^2=\frac{7}{4}$.

Möbius transformation from a unit disc to its complement

If $z = (1+\cos a) +i \sin a$ and $a ∈ (0,2π)$, Then find $arg(z)$

Rotate sine wave on complex plane

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