Question

Show $\left|\int_{|z - R| = R} z^{14}\, dz \right| \leq 2^{15} \pi R^{15}$

score 75 · Answer 1 · 2020-06-26 18:18:28

75

Views

Show $\left|\int_{|z - R| = R} z^{14}\, dz \right| \leq 2^{15} \pi R^{15}$

Published on 26 Jun 2020 - 18:18

score 80 · Answer 2 · 2020-06-26 19:26:50

80

Views

If Γ is a closed Jordan curve that encloses a region with area A, show that $A=\frac{1}{2i} \int_{\Gamma} \overline{z}dz$.

Published on 26 Jun 2020 - 19:26

score 147 · Answer 3 · 2020-06-26 19:51:47

147

Views

Easier approach to $\int_0^{\infty} \frac{\mathrm{e}^{-x} \cosh(2x/5)}{1 + \mathrm{e}^{-2x}} \, \mathrm{d}x$?

Published on 26 Jun 2020 - 19:51

score 279 · Answer 4 · 2020-06-28 03:33:55

279

Views

Evaluate using Residues $\int_0^{2\pi}\frac{d\theta}{1+a\sin\theta}$

Published on 28 Jun 2020 - 3:33

score 80 · Answer 5 · 2020-06-28 08:36:30

80

Views

Calculate $\int_{|z|=2}\frac{1}{\sqrt{z^4+4z+1}}$

Published on 28 Jun 2020 - 8:36

score 61 · Answer 6 · 2020-06-29 07:33:43

61

Views

Given a square $\gamma$ with vertices at $\pm 2,\pm2i$ Calculate $\int_{\gamma}\frac{z}{\sqrt{1+z+z^4}}dz$

Published on 29 Jun 2020 - 7:33

score 110 · Answer 7 · 2020-06-29 11:47:31

110

Views

Integral of $\int_{-\infty}^{\infty} e^{\alpha x}/({e^x+1})$

Published on 29 Jun 2020 - 11:47

score 85 · Answer 8 · 2020-06-30 20:15:37

85

Views

Good revision notes for complex variable and linear algebra

Published on 30 Jun 2020 - 20:15

score 34 · Answer 9 · 2026-03-28 10:35:00

34

Views

integration over surface in $\Bbb C^2$ parametrized with 3 parameters

Published on 28 Mar 2026 - 10:35

score 86 · Answer 10 · 2026-03-26 18:50:43

86

Views

Solve $\int_{|z|=5} \frac{z^2}{(z-3i)(z-3i)}$

Published on 26 Mar 2026 - 18:50

score 65 · Answer 11 · 2026-03-26 18:51:52

65

Views

How does $\frac{1}{2\pi i}\int_{|z|=3} \frac{e^{zt}}{z^2+1}dz=sin(t)$ when $t>0$?

Published on 26 Mar 2026 - 18:51

score 88 · Answer 12 · 2026-03-26 03:09:33

88

Views

Using Cauchy's theorem

Published on 26 Mar 2026 - 3:09

score 152 · Answer 13 · 2020-07-05 15:47:03

152

Views

If $f$ is holomorphic then integral of $f'(z)\overline{f(z)}$ on a close line is an imaginary number.

Published on 05 Jul 2020 - 15:47

score 279 · Answer 14 · 2020-07-05 20:18:35

279

Views

Find the average value of $x^2 - y^2 + 2y$ over the circle $|z - 5 + 2i| = 3$.

Published on 05 Jul 2020 - 20:18

score 35 · Answer 15 · 2026-03-25 16:06:08

35

Views

Why does this improper integral converge

Published on 25 Mar 2026 - 16:06

List Question

Show $\left|\int_{|z - R| = R} z^{14}\, dz \right| \leq 2^{15} \pi R^{15}$

If Γ is a closed Jordan curve that encloses a region with area A, show that $A=\frac{1}{2i} \int_{\Gamma} \overline{z}dz$.

Easier approach to $\int_0^{\infty} \frac{\mathrm{e}^{-x} \cosh(2x/5)}{1 + \mathrm{e}^{-2x}} \, \mathrm{d}x$?

Evaluate using Residues $\int_0^{2\pi}\frac{d\theta}{1+a\sin\theta}$

Calculate $\int_{|z|=2}\frac{1}{\sqrt{z^4+4z+1}}$

Given a square $\gamma$ with vertices at $\pm 2,\pm2i$ Calculate $\int_{\gamma}\frac{z}{\sqrt{1+z+z^4}}dz$

Integral of $\int_{-\infty}^{\infty} e^{\alpha x}/({e^x+1})$

Good revision notes for complex variable and linear algebra

integration over surface in $\Bbb C^2$ parametrized with 3 parameters

Solve $\int_{|z|=5} \frac{z^2}{(z-3i)(z-3i)}$

How does $\frac{1}{2\pi i}\int_{|z|=3} \frac{e^{zt}}{z^2+1}dz=sin(t)$ when $t>0$?

Using Cauchy's theorem

If $f$ is holomorphic then integral of $f'(z)\overline{f(z)}$ on a close line is an imaginary number.

Find the average value of $x^2 - y^2 + 2y$ over the circle $|z - 5 + 2i| = 3$.

Why does this improper integral converge

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