Question

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

score 483 · Answer 1 · 2026-05-04 03:56:31

483

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 04 May 2026 - 3:56

score 351 · Answer 2 · 2026-05-04 03:58:25

351

Views

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

Published on 04 May 2026 - 3:58

score 101 · Answer 3 · 2026-05-04 03:56:31

101

Views

Cauchy-Riemann Equations the existence of partial derivatives

Published on 04 May 2026 - 3:56

score 75 · Answer 4 · 2026-05-04 03:58:27

75

Views

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

Published on 04 May 2026 - 3:58

score 10k · Answer 5 · 2026-05-04 03:56:31

10k

Views

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

Published on 04 May 2026 - 3:56

score 4.9k · Answer 6 · 2026-05-04 03:56:41

4.9k

Views

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

Published on 04 May 2026 - 3:56

score 487 · Answer 7 · 2026-05-04 03:58:26

487

Views

Satisfying Cauchy Riemann equations at discontinuity

Published on 04 May 2026 - 3:58

score 8.7k · Answer 8 · 2026-04-26 08:02:56

8.7k

Views

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

Published on 26 Apr 2026 - 8:02

score 1.5k · Answer 9 · 2026-03-27 21:01:33

1.5k

Views

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

Published on 27 Mar 2026 - 21:01

score 276 · Answer 10 · 2026-04-08 12:09:42

276

Views

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

Published on 08 Apr 2026 - 12:09

score 63 · Answer 11 · 2026-04-28 11:36:47

63

Views

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

Published on 28 Apr 2026 - 11:36

score 98 · Answer 12 · 2026-04-20 09:50:56

98

Views

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

Published on 20 Apr 2026 - 9:50

score 41 · Answer 13 · 2026-05-02 04:03:13

41

Views

Two different forms of Cauchy-Riemann equation:

Published on 02 May 2026 - 4:03

score 121 · Answer 14 · 2026-04-29 09:07:01

121

Views

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

Published on 29 Apr 2026 - 9:07

score 37 · Answer 15 · 2026-05-07 11:33:06

37

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 07 May 2026 - 11:33

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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