Question

Is $f(x + iy) = \exp(iy)$ analytic?

score 140 · Answer 1 · 2022-01-21 16:01:51

140

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Is $f(x + iy) = \exp(iy)$ analytic?

Published on 21 Jan 2022 - 16:01

score 39 · Answer 2 · 2022-01-24 16:17:33

39

Views

Is this function complex differentiable?

Published on 24 Jan 2022 - 16:17

score 87 · Answer 3 · 2022-01-28 22:33:49

87

Views

Cauchy-Riemann equations and holomorphic functions

Published on 28 Jan 2022 - 22:33

score 84 · Answer 4 · 2022-01-29 21:29:05

84

Views

Complex functions that is not quite analytic

Published on 29 Jan 2022 - 21:29

score 656 · Answer 5 · 2022-02-01 22:46:56

656

Views

Given the harmonic function u(x,y), find its harmonic conjugate v(x,y) then express the analytics function f(z) in terms of z

Published on 01 Feb 2022 - 22:46

score 94 · Answer 6 · 2022-02-07 21:53:48

94

Views

Show that complex function satisfies Cauchy-Riemann equations at z=1 but is not differentiable there.

Published on 07 Feb 2022 - 21:53

score 184 · Answer 7 · 2022-02-23 03:54:36

184

Views

When does ∫()=∫(())?

Published on 23 Feb 2022 - 3:54

score 105 · Answer 8 · 2022-03-07 08:33:21

105

Views

Let $f$ be holomorphic on connected open set $D$. Prove $u^4+v^4$ being constant implies $f=u+iv$ being constant.

Published on 07 Mar 2022 - 8:33

score 93 · Answer 9 · 2022-03-14 02:42:32

93

Views

Finding the analytic function of $z$, given the real part

Published on 14 Mar 2022 - 2:42

score 25 · Answer 10 · 2022-04-03 12:04:41

25

Views

Finding all differentiable complex functions satisfying given conditions.

Published on 03 Apr 2022 - 12:04

score 301 · Answer 11 · 2022-04-05 10:26:56

301

Views

Determine at what points the complex function $f\left(z\right)=e^{2x}\cos3x+ie^{3x}\sin2y$ is differentiable.

Published on 05 Apr 2022 - 10:26

score 75 · Answer 12 · 2022-04-13 12:21:08

75

Views

Find the continuous function $f$ with domain $\mathbb C$ such that it's differentiable on $x^2-y^2=1$ but is not differentiable at other points

Published on 13 Apr 2022 - 12:21

score 64 · Answer 13 · 2022-04-17 21:51:41

64

Views

Question about Cauchy Conditions from History Section of Remmert's Textbook

Published on 17 Apr 2022 - 21:51

score 474 · Answer 14 · 2022-04-20 06:37:17

474

Views

Verify that $\sqrt z$ is analytic using the Cauchy–Riemann equations

Published on 20 Apr 2022 - 6:37

score 45 · Answer 15 · 2026-02-23 20:43:18

45

Views

Given $f(z) = |z|^{z_1}$, what is $ f'{(z)}$.

Published on 23 Feb 2026 - 20:43

List Question

Is $f(x + iy) = \exp(iy)$ analytic?

Is this function complex differentiable?

Cauchy-Riemann equations and holomorphic functions

Complex functions that is not quite analytic

Given the harmonic function u(x,y), find its harmonic conjugate v(x,y) then express the analytics function f(z) in terms of z

Show that complex function satisfies Cauchy-Riemann equations at z=1 but is not differentiable there.

When does ∫()=∫(())?

Let $f$ be holomorphic on connected open set $D$. Prove $u^4+v^4$ being constant implies $f=u+iv$ being constant.

Finding the analytic function of $z$, given the real part

Finding all differentiable complex functions satisfying given conditions.

Determine at what points the complex function $f\left(z\right)=e^{2x}\cos3x+ie^{3x}\sin2y$ is differentiable.

Find the continuous function $f$ with domain $\mathbb C$ such that it's differentiable on $x^2-y^2=1$ but is not differentiable at other points

Question about Cauchy Conditions from History Section of Remmert's Textbook

Verify that $\sqrt z$ is analytic using the Cauchy–Riemann equations

Given $f(z) = |z|^{z_1}$, what is $ f'{(z)}$.

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