Question

Can a) and b) real components of an complex equation?

score 93 · Answer 1 · 2023-05-13 19:04:12

93

Views

Can a) and b) real components of an complex equation?

Published on 13 May 2023 - 19:04

score 358 · Answer 2 · 2023-05-27 15:52:47

358

Views

Find conjugate harmonic function of $u=x^2+y^2$?

Published on 27 May 2023 - 15:52

score 32 · Answer 3 · 2023-06-01 08:44:01

32

Views

Differentiabilty of Complex Function

Published on 01 Jun 2023 - 8:44

score 132 · Answer 4 · 2023-07-08 13:11:51

132

Views

Minimum and maximum of $|f(z)|$, analytic but doesn't satisfy Cauchy-Riemann

Published on 08 Jul 2023 - 13:11

score 215 · Answer 5 · 2023-07-09 08:40:23

215

Views

Іs there any relationship between $v(y)$ and $u(y)$ where $f(iy) = u(y) + iv(y)$?

Published on 09 Jul 2023 - 8:40

score 80 · Answer 6 · 2023-07-24 23:57:16

80

Views

What holomorphic functions $f = u + iv$ satisfy $u(x, y) = x^3 + xg(y)$, where $g$ is a twice continuously differentiable function?

Published on 24 Jul 2023 - 23:57

score 85 · Answer 7 · 2023-08-20 14:57:21

85

Views

Is this function holomorphic in $z = 0$?

Published on 20 Aug 2023 - 14:57

score 416 · Answer 8 · 2023-08-23 14:07:21

416

Views

Prove an entire function is constant on complex plane

Published on 23 Aug 2023 - 14:07

score 53 · Answer 9 · 2023-08-23 15:21:55

53

Views

Must Cauchy–Riemann equation hold if we only know that the partial derivatives exist?

Published on 23 Aug 2023 - 15:21

score 289 · Answer 10 · 2023-09-09 16:17:27

289

Views

Let function $f=u +iv$ is analytic on $D$ and for some $a,b,c \in \mathbb R$, $a^2+b^2 \neq 0$ and $au+bv=c$ on $D$. Prove that $f$ is constant on $D$

Published on 09 Sep 2023 - 16:17

score 78 · Answer 11 · 2023-09-18 17:19:47

78

Views

Must every Cauchy-Riemann condition be fulfilled simultaneously?

Published on 18 Sep 2023 - 17:19

score 71 · Answer 12 · 2023-09-23 15:38:07

71

Views

Cauchy Riemann using polar form of $f(z)$? (NOT polar form of $z$)

Published on 23 Sep 2023 - 15:38

score 47 · Answer 13 · 2023-09-27 11:14:11

47

Views

Can you use the Cauchy-Riemann equations to show that a complex function $f(z)$ has an analytical antiderivative?

Published on 27 Sep 2023 - 11:14

score 48 · Answer 14 · 2026-03-25 23:10:37

48

Views

Weaker version of Goursats theroem

Published on 25 Mar 2026 - 23:10

score 50 · Answer 15 · 2023-10-25 23:25:32

50

Views

3D / nD version of "amplitwist" (Drehstreckung) property of holomorphic functions?

Published on 25 Oct 2023 - 23:25

List Question

Can a) and b) real components of an complex equation?

Find conjugate harmonic function of $u=x^2+y^2$?

Differentiabilty of Complex Function

Minimum and maximum of $|f(z)|$, analytic but doesn't satisfy Cauchy-Riemann

Іs there any relationship between $v(y)$ and $u(y)$ where $f(iy) = u(y) + iv(y)$?

What holomorphic functions $f = u + iv$ satisfy $u(x, y) = x^3 + xg(y)$, where $g$ is a twice continuously differentiable function?

Is this function holomorphic in $z = 0$?

Prove an entire function is constant on complex plane

Must Cauchy–Riemann equation hold if we only know that the partial derivatives exist?

Let function $f=u +iv$ is analytic on $D$ and for some $a,b,c \in \mathbb R$, $a^2+b^2 \neq 0$ and $au+bv=c$ on $D$. Prove that $f$ is constant on $D$

Must every Cauchy-Riemann condition be fulfilled simultaneously?

Cauchy Riemann using polar form of $f(z)$? (NOT polar form of $z$)

Can you use the Cauchy-Riemann equations to show that a complex function $f(z)$ has an analytical antiderivative?

Weaker version of Goursats theroem

3D / nD version of "amplitwist" (Drehstreckung) property of holomorphic functions?

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