Question

$\sum_{n=0}^N |b_n|^2 r^{2n}=\int_{-\pi}^{\pi}|f(z_0+re^{in\theta})|^2d\theta$

score 92 · Answer 1 · 2026-04-16 07:01:11

92

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$\sum_{n=0}^N |b_n|^2 r^{2n}=\int_{-\pi}^{\pi}|f(z_0+re^{in\theta})|^2d\theta$

Published on 16 Apr 2026 - 7:01

score 1.1k · Answer 2 · 2026-03-25 01:16:18

1.1k

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Find a Mobius Transformation that maps the points $\{0,1,\infty\}$ to $\{-1,-i,1\}$

Published on 25 Mar 2026 - 1:16

score 52 · Answer 3 · 2026-04-12 07:16:20

52

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Showing a class of subharmonic functions are bounded by 0

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score 192 · Answer 4 · 2026-04-14 17:08:50

192

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Why is $z=\infty$ not a branch point of the Inverse Joukowski map

Published on 14 Apr 2026 - 17:08

score 298 · Answer 5 · 2026-03-25 06:10:32

298

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Use the Cauchy Integral Formula to evaluate the integral

Published on 25 Mar 2026 - 6:10

score 161 · Answer 6 · 2026-04-15 02:26:27

161

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Find Roots of $x^3-7$ Relative to Roots of Unity and $\sqrt{7}$

Published on 15 Apr 2026 - 2:26

score 68 · Answer 7 · 2026-04-13 16:51:54

68

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Argument of a general Complex number

Published on 13 Apr 2026 - 16:51

score 86 · Answer 8 · 2026-04-17 09:18:00

86

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Why $\Re\left(e^{\sqrt{-\log x}}\right)=\Im\left(e^{\sqrt{-\log x}}\right)$ has no real solutions?

Published on 17 Apr 2026 - 9:18

score 630 · Answer 9 · 2026-04-10 02:56:08

630

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Question about essential singularity

Published on 10 Apr 2026 - 2:56

score 1k · Answer 10 · 2026-03-25 06:13:13

1k

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Use the Cauchy Integral Formula to evaluate the following integral: $\int \frac{e^z \,dz}{z^2+1}$

Published on 25 Mar 2026 - 6:13

score 272 · Answer 11 · 2026-04-14 20:14:46

272

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Prove $|f'(z)|\leq\frac{Re(f(z))}{Re(z)}$ for all $z$ in the right half plane

Published on 14 Apr 2026 - 20:14

score 67 · Answer 12 · 2026-04-11 09:53:01

67

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complex line equation

Published on 11 Apr 2026 - 9:53

score 69 · Answer 13 · 2026-04-15 14:09:23

Prove that for all $a,b \in \mathbb{D}$ that $\left|\frac{f(a)-f(b)}{1-\overline{f(b)}f(a)}\right|\le\left |\frac{a-b}{1-\bar{b}a}\right|$

score 320 · Answer 14 · 2026-04-11 16:01:38

320

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Use the Cauchy Integral Formula to evaluate the following integrals:

Published on 11 Apr 2026 - 16:01

score 224 · Answer 15 · 2026-04-11 16:40:34

224

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Multiple roots of one polynomial of degree 4

Published on 11 Apr 2026 - 16:40

List Question

$\sum_{n=0}^N |b_n|^2 r^{2n}=\int_{-\pi}^{\pi}|f(z_0+re^{in\theta})|^2d\theta$

Find a Mobius Transformation that maps the points $\{0,1,\infty\}$ to $\{-1,-i,1\}$

Showing a class of subharmonic functions are bounded by 0

Why is $z=\infty$ not a branch point of the Inverse Joukowski map

Use the Cauchy Integral Formula to evaluate the integral

Find Roots of $x^3-7$ Relative to Roots of Unity and $\sqrt{7}$

Argument of a general Complex number

Why $\Re\left(e^{\sqrt{-\log x}}\right)=\Im\left(e^{\sqrt{-\log x}}\right)$ has no real solutions?

Question about essential singularity

Use the Cauchy Integral Formula to evaluate the following integral: $\int \frac{e^z \,dz}{z^2+1}$

Prove $|f'(z)|\leq\frac{Re(f(z))}{Re(z)}$ for all $z$ in the right half plane

complex line equation

Prove that for all $a,b \in \mathbb{D}$ that $\left|\frac{f(a)-f(b)}{1-\overline{f(b)}f(a)}\right|\le\left |\frac{a-b}{1-\bar{b}a}\right|$

Use the Cauchy Integral Formula to evaluate the following integrals:

Multiple roots of one polynomial of degree 4

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