Question

Proving that holomorphic functions which map the real axis to the imaginary axis also map the imaginary axis to the real axis.

score 481 · Answer 1 · 2026-03-21 19:33:02

481

Views

Proving that holomorphic functions which map the real axis to the imaginary axis also map the imaginary axis to the real axis.

Published on 21 Mar 2026 - 19:33

score 348 · Answer 2 · 2026-03-22 08:32:18

348

Views

Proof of Cauchy–Riemann equations being same as $\frac{\partial f}{\partial \bar z}=0$

Published on 22 Mar 2026 - 8:32

score 99 · Answer 3 · 2026-03-21 22:24:45

99

Views

Cauchy-Riemann Equations the existence of partial derivatives

Published on 21 Mar 2026 - 22:24

score 72 · Answer 4 · 2026-03-22 12:01:14

72

Views

Cauchy-Riemann equations - a doubt about the proof on MathWorld

Published on 22 Mar 2026 - 12:01

score 10k · Answer 5 · 2026-03-21 16:21:59

10k

Views

Showing that $|z|^2$ is nowhere analytic

Published on 21 Mar 2026 - 16:21

score 4.9k · Answer 6 · 2026-03-22 04:42:11

4.9k

Views

Show that the Cauchy-Riemann equations are satisfied at the origin but $f$ is not analytic.

Published on 22 Mar 2026 - 4:42

score 484 · Answer 7 · 2026-03-22 12:24:39

484

Views

Satisfying Cauchy Riemann equations at discontinuity

Published on 22 Mar 2026 - 12:24

score 8.7k · Answer 8 · 2026-03-25 09:28:43

8.7k

Views

Cauchy Riemann $e^{z^2}$.

Published on 25 Mar 2026 - 9:28

score 1.5k · Answer 9 · 2026-02-23 10:29:23

1.5k

Views

if $u$ is a harmonic function, then $u$ has a harmonic conjugate.

Published on 23 Feb 2026 - 10:29

score 274 · Answer 10 · 2019-10-23 10:53:59

274

Views

Extending a Real Function $u$ to a Holomorphic Function: Must $f(\mathbb{R})= u(\mathbb{R})$?

Published on 23 Oct 2019 - 10:53

score 60 · Answer 11 · 2019-11-06 13:33:04

60

Views

Find an expression for $f(z)$ using Cauchy-Riemann Equations:

Published on 06 Nov 2019 - 13:33

score 97 · Answer 12 · 2019-11-07 02:24:08

97

Views

Let $z = x + iy$, then $f(x) = x^2 - y^2$ is this analytic?

Published on 07 Nov 2019 - 2:24

score 40 · Answer 13 · 2026-03-03 04:01:57

40

Views

Two different forms of Cauchy-Riemann equation:

Published on 03 Mar 2026 - 4:01

score 120 · Answer 14 · 2019-11-08 12:31:11

120

Views

Complex Differentiability of $f(x+iy)=\frac{(1+i)x^3-(1-i)y^3}{x^2+y^2}$

Published on 08 Nov 2019 - 12:31

score 36 · Answer 15 · 2019-11-17 10:58:58

36

Views

The integer function $f(z) = u(x,y) + iv(x, y)$ is such that $u(x, y) = e^{−x}\sin(y -1) + y$. What's the value of $f'(i)$?

Published on 17 Nov 2019 - 10:58

List Question

Proving that holomorphic functions which map the real axis to the imaginary axis also map the imaginary axis to the real axis.

Proof of Cauchy–Riemann equations being same as $\frac{\partial f}{\partial \bar z}=0$

Cauchy-Riemann Equations the existence of partial derivatives

Cauchy-Riemann equations - a doubt about the proof on MathWorld

Showing that $|z|^2$ is nowhere analytic

Show that the Cauchy-Riemann equations are satisfied at the origin but $f$ is not analytic.

Satisfying Cauchy Riemann equations at discontinuity

Cauchy Riemann $e^{z^2}$.

if $u$ is a harmonic function, then $u$ has a harmonic conjugate.

Extending a Real Function $u$ to a Holomorphic Function: Must $f(\mathbb{R})= u(\mathbb{R})$?

Find an expression for $f(z)$ using Cauchy-Riemann Equations:

Let $z = x + iy$, then $f(x) = x^2 - y^2$ is this analytic?

Two different forms of Cauchy-Riemann equation:

Complex Differentiability of $f(x+iy)=\frac{(1+i)x^3-(1-i)y^3}{x^2+y^2}$

The integer function $f(z) = u(x,y) + iv(x, y)$ is such that $u(x, y) = e^{−x}\sin(y -1) + y$. What's the value of $f'(i)$?

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