Question

Prove that if all of the roots of a polynomial $P(z)$ are real, then for any $b$ the roots of the polynomial $R(z)=P(z+ib)+P(z-ib)$ are also real.

score 737 · Answer 1 · 2026-04-03 13:28:31

737

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Prove that if all of the roots of a polynomial $P(z)$ are real, then for any $b$ the roots of the polynomial $R(z)=P(z+ib)+P(z-ib)$ are also real.

Published on 03 Apr 2026 - 13:28

score 347 · Answer 2 · 2026-04-02 01:53:49

347

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computing $A_2=\sum_{k=1}^{n}\frac{1}{(z_k-1)^2} $ and $\sum_{k=1}^n \cot^2\left( \frac{k\pi}{n+1}\right)$

Published on 02 Apr 2026 - 1:53

score 92 · Answer 3 · 2026-04-06 10:50:53

92

Views

For what values of $z$ is $\sum_{n=0}^\infty\frac{z^n}{1+z^{2n}}$ convergent?

Published on 06 Apr 2026 - 10:50

score 55 · Answer 4 · 2026-04-10 14:19:58

55

Views

Transformation function in complex

Published on 10 Apr 2026 - 14:19

score 28 · Answer 5 · 2026-03-25 03:02:47

28

Views

$ g\in C^{2}(\Omega)$ are dense in $f\in C(\partial\Omega)$?

Published on 25 Mar 2026 - 3:02

score 118 · Answer 6 · 2026-04-09 02:42:51

118

Views

Exercise 34 from Needham Visual Complex Analysis 1. Cyclotomic polynomial for the pth (p prime )root of unity

Published on 09 Apr 2026 - 2:42

score 178 · Answer 7 · 2026-04-01 04:29:03

178

Views

Solving absolute value equation in complex numbers

Published on 01 Apr 2026 - 4:29

score 1.9k · Answer 8 · 2026-04-09 01:53:14

1.9k

Views

Complex potentials and gradient

Published on 09 Apr 2026 - 1:53

score 203 · Answer 9 · 2026-04-08 22:41:43

203

Views

Solve the improper integral with techniques of complex analysis

Published on 08 Apr 2026 - 22:41

score 845 · Answer 10 · 2026-04-06 21:39:31

845

Views

Finding an harmonic function

Published on 06 Apr 2026 - 21:39

score 81 · Answer 11 · 2026-04-10 00:56:23

81

Views

Study of a " flow "

Published on 10 Apr 2026 - 0:56

score 125 · Answer 12 · 2026-03-25 07:40:37

125

Views

Combining strictly positive numbers to complex powers?

Published on 25 Mar 2026 - 7:40

score 77 · Answer 13 · 2026-04-10 05:03:09

77

Views

How to Define a Horizontal Complex Function

Published on 10 Apr 2026 - 5:03

score 103 · Answer 14 · 2018-01-23 05:29:06

103

Views

Show that $\dfrac{\partial(fg)}{\partial z}=\dfrac{\partial(f)}{\partial z}g+f\dfrac{\partial(g)}{\partial z}$

Published on 23 Jan 2018 - 5:29

score 45 · Answer 15 · 2026-03-25 17:40:43

45

Views

How to find the roots of this polynomial over $\mathbb{C}$?

Published on 25 Mar 2026 - 17:40

List Question

Prove that if all of the roots of a polynomial $P(z)$ are real, then for any $b$ the roots of the polynomial $R(z)=P(z+ib)+P(z-ib)$ are also real.

computing $A_2=\sum_{k=1}^{n}\frac{1}{(z_k-1)^2} $ and $\sum_{k=1}^n \cot^2\left( \frac{k\pi}{n+1}\right)$

For what values of $z$ is $\sum_{n=0}^\infty\frac{z^n}{1+z^{2n}}$ convergent?

Transformation function in complex

$ g\in C^{2}(\Omega)$ are dense in $f\in C(\partial\Omega)$?

Exercise 34 from Needham Visual Complex Analysis 1. Cyclotomic polynomial for the pth (p prime )root of unity

Solving absolute value equation in complex numbers

Complex potentials and gradient

Solve the improper integral with techniques of complex analysis

Finding an harmonic function

Study of a " flow "

Combining strictly positive numbers to complex powers?

How to Define a Horizontal Complex Function

Show that $\dfrac{\partial(fg)}{\partial z}=\dfrac{\partial(f)}{\partial z}g+f\dfrac{\partial(g)}{\partial z}$

How to find the roots of this polynomial over $\mathbb{C}$?

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