Question

Finding The Complex Roots Of $4z^5 + \overline z^3= 0$?

score 52 · Answer 1 · 2026-04-15 11:33:22

52

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Finding The Complex Roots Of $4z^5 + \overline z^3= 0$?

Published on 15 Apr 2026 - 11:33

score 377 · Answer 2 · 2026-04-13 11:20:26

377

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Derivative of the complex norm as commonly used in physics

Published on 13 Apr 2026 - 11:20

score 99 · Answer 3 · 2026-04-15 00:59:58

99

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Knowing $|z|$ and $|w|$ (and possibly $z\overline{w}$), what are $|z+w|^2$, $|zw|^2$, $|z-w|^2$, $|z/w|^2$?

Published on 15 Apr 2026 - 0:59

score 118 · Answer 4 · 2026-05-14 08:42:22

118

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Root of Complex Number in Polar Representation with Negative "r"

Published on 14 May 2026 - 8:42

score 163 · Answer 5 · 2026-03-25 11:23:36

163

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Let $a\in\mathbb{C}, |a|=1$ and $c$ an irrational real number. Prove: $a^c$ is dense in the unit circle.

Published on 25 Mar 2026 - 11:23

score 52 · Answer 6 · 2026-04-13 12:33:34

52

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Why $\frac{\partial}{\partial \bar{z}} I(z)=\oint_{\gamma} \frac{\partial}{\partial \bar{z}}\left(\frac{1}{\zeta-z}\right) d \zeta$?

Published on 13 Apr 2026 - 12:33

score 103 · Answer 7 · 2026-04-17 08:53:16

103

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Calculating $\binom{99}{0}+ \binom{100}{2}+ \binom{99}{3}+ \binom{100}{5}+ \binom{99}{6}+ \binom{100}{8}+ ..+ \binom{100}{98}+\binom{99}{99}$

Published on 17 Apr 2026 - 8:53

score 156 · Answer 8 · 2026-04-14 06:28:55

156

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Proof? of irreducibility of cyclotomic polynomial

Published on 14 Apr 2026 - 6:28

score 43 · Answer 9 · 2026-04-13 01:04:20

43

Views

$\ A+A=\{3i,3+2i,3+4i\}$. find A

Published on 13 Apr 2026 - 1:04

score 64 · Answer 10 · 2026-04-15 06:33:30

64

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Complex polynomial whose roots contain the fifth roots of another complex number

Published on 15 Apr 2026 - 6:33

score 190 · Answer 11 · 2026-05-11 03:14:03

190

Views

A curious property of exponential sums for rational polynomials?

Published on 11 May 2026 - 3:14

score 43 · Answer 12 · 2026-04-24 15:56:41

43

Views

Suppose that $z = x + iy$, with $y > 0$. Show that there are positive real numbers $u$ and $v$ with $2u^{2} = |z| + x$ and $2v^{2} = |z| - x$

Published on 24 Apr 2026 - 15:56

score 126 · Answer 13 · 2026-04-16 12:43:13

126

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Show that if $|z| < 1$, then $\displaystyle\frac{z}{1+z} + \frac{2z^{2}}{1+z^{2}} + \frac{4z^{4}}{1+z^{4}} + \frac{8z^{8}}{1+z^{8}} + \ldots$

Published on 16 Apr 2026 - 12:43

score 308 · Answer 14 · 2026-04-17 14:42:45

308

Views

Find all polynomials satisfying $p(x)p(-x)=p(x^2)$

Published on 17 Apr 2026 - 14:42

score 297 · Answer 15 · 2026-04-11 10:56:36

297

Views

Simplify $|e^{2iwt} - 1|$

Published on 11 Apr 2026 - 10:56

List Question

Finding The Complex Roots Of $4z^5 + \overline z^3= 0$?

Derivative of the complex norm as commonly used in physics

Knowing $|z|$ and $|w|$ (and possibly $z\overline{w}$), what are $|z+w|^2$, $|zw|^2$, $|z-w|^2$, $|z/w|^2$?

Root of Complex Number in Polar Representation with Negative "r"

Let $a\in\mathbb{C}, |a|=1$ and $c$ an irrational real number. Prove: $a^c$ is dense in the unit circle.

Why $\frac{\partial}{\partial \bar{z}} I(z)=\oint_{\gamma} \frac{\partial}{\partial \bar{z}}\left(\frac{1}{\zeta-z}\right) d \zeta$?

Calculating $\binom{99}{0}+ \binom{100}{2}+ \binom{99}{3}+ \binom{100}{5}+ \binom{99}{6}+ \binom{100}{8}+ ..+ \binom{100}{98}+\binom{99}{99}$

Proof? of irreducibility of cyclotomic polynomial

$\ A+A=\{3i,3+2i,3+4i\}$. find A

Complex polynomial whose roots contain the fifth roots of another complex number

A curious property of exponential sums for rational polynomials?

Suppose that $z = x + iy$, with $y > 0$. Show that there are positive real numbers $u$ and $v$ with $2u^{2} = |z| + x$ and $2v^{2} = |z| - x$

Show that if $|z| < 1$, then $\displaystyle\frac{z}{1+z} + \frac{2z^{2}}{1+z^{2}} + \frac{4z^{4}}{1+z^{4}} + \frac{8z^{8}}{1+z^{8}} + \ldots$

Find all polynomials satisfying $p(x)p(-x)=p(x^2)$

Simplify $|e^{2iwt} - 1|$

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