Question

Efficient way to solve homogenous system with complex numbers?

score 50 · Answer 1 · 2026-04-10 14:11:44

50

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Efficient way to solve homogenous system with complex numbers?

Published on 10 Apr 2026 - 14:11

score 101 · Answer 2 · 2026-04-15 21:12:17

101

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Is $(2+i)^n + (2-i)^n $ a real number ($\in \Bbb R$)?

Published on 15 Apr 2026 - 21:12

score 56 · Answer 3 · 2026-04-15 22:03:11

56

Views

If $z_0$ is a solution for $z^{13}-13z^7+7z^3-3z+1=0$, does also $\bar z_0$ is a solution?

Published on 15 Apr 2026 - 22:03

score 53 · Answer 4 · 2026-04-16 01:32:19

53

Views

Compare two complex numbers of trigonometric form in solving $z^4-16\bar{z}^2 = 0$

Published on 16 Apr 2026 - 1:32

score 459 · Answer 5 · 2026-04-13 12:28:39

459

Views

Roots of complex number (2018 AMC 12A Problem 22)

Published on 13 Apr 2026 - 12:28

score 444 · Answer 6 · 2026-04-12 09:19:51

444

Views

Show that the complex $\cos$ function has only real roots

Published on 12 Apr 2026 - 9:19

score 695 · Answer 7 · 2026-04-15 23:32:07

695

Views

Find the number of zeros of $z^{3}+2z^{2}-z-2+e^{z}$ which lies in the left half plane

Published on 15 Apr 2026 - 23:32

score 48 · Answer 8 · 2026-04-16 14:42:32

48

Views

Is there some $f_{2,3}:\Bbb R^+\to S^1$ such that $f_{2,3}(x)=f_{2,3}(2x)=f_{2,3}(3x)$?

Published on 16 Apr 2026 - 14:42

score 99 · Answer 9 · 2026-04-15 10:01:11

99

Views

Identifying when $i^n$ (for integer $n$) is $1$, $-1$, $i$, $-i$

Published on 15 Apr 2026 - 10:01

score 1k · Answer 10 · 2026-04-15 10:04:15

1k

Views

If $\alpha, \beta, \gamma, \delta$ are distinct roots of equation $x^4 + x^2 + 1 = 0$ then $\alpha^6 + \beta^6 + \gamma^6 + \delta^6$ is

Published on 15 Apr 2026 - 10:04

score 94 · Answer 11 · 2026-04-13 07:17:59

94

Views

What is $\frac{d}{dx}x^i$?

Published on 13 Apr 2026 - 7:17

score 125 · Answer 12 · 2026-04-09 16:44:46

125

Views

Complex derivatives

Published on 09 Apr 2026 - 16:44

score 80 · Answer 13 · 2026-04-14 18:46:12

80

Views

Obtain $z_1,z_2$ and $z_1/z_2$

Published on 14 Apr 2026 - 18:46

score 64 · Answer 14 · 2026-04-15 05:00:39

64

Views

Reconciling Behavior of $e^t$ and $e^{it}$ as $t$ goes to infinity

Published on 15 Apr 2026 - 5:00

score 191 · Answer 15 · 2026-03-27 12:55:59

191

Views

Arguments and complex roots of unity

Published on 27 Mar 2026 - 12:55

List Question

Efficient way to solve homogenous system with complex numbers?

Is $(2+i)^n + (2-i)^n $ a real number ($\in \Bbb R$)?

If $z_0$ is a solution for $z^{13}-13z^7+7z^3-3z+1=0$, does also $\bar z_0$ is a solution?

Compare two complex numbers of trigonometric form in solving $z^4-16\bar{z}^2 = 0$

Roots of complex number (2018 AMC 12A Problem 22)

Show that the complex $\cos$ function has only real roots

Find the number of zeros of $z^{3}+2z^{2}-z-2+e^{z}$ which lies in the left half plane

Is there some $f_{2,3}:\Bbb R^+\to S^1$ such that $f_{2,3}(x)=f_{2,3}(2x)=f_{2,3}(3x)$?

Identifying when $i^n$ (for integer $n$) is $1$, $-1$, $i$, $-i$

If $\alpha, \beta, \gamma, \delta$ are distinct roots of equation $x^4 + x^2 + 1 = 0$ then $\alpha^6 + \beta^6 + \gamma^6 + \delta^6$ is

What is $\frac{d}{dx}x^i$?

Complex derivatives

Obtain $z_1,z_2$ and $z_1/z_2$

Reconciling Behavior of $e^t$ and $e^{it}$ as $t$ goes to infinity

Arguments and complex roots of unity

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