List questions from complex-numbers

Published on 15 Apr 2026 - 5:07

77

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Find the polynomial $P(x)$ s.t. for any $a,b\in\Bbb C$ s.t. $a^2+b^2=ab$, $P(a+b)=6\big(P(a)+P(b)\big)+15a^2b^2(a+b)$.

Published on 16 Apr 2026 - 22:55

71

Views

Which complex numbers satisfy $(-1)^z=1$ and $(-1)^z=-1$?

Published on 16 Apr 2026 - 9:20

255

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Factoring $z^4+64=0$

Published on 15 Apr 2026 - 11:12

70

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Explaining why $i^n$ can only be equal to $1,i,-1,-i$

Published on 14 Apr 2026 - 5:16

53

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Set of points $\left| \frac{z+i\bar z}{2}\right|=\left| z-\frac{1+i}{2}\right|$

Published on 17 Apr 2026 - 5:33

50

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Integration - substitution that introduces $i$ into the integrand

Published on 12 Apr 2026 - 5:26

45

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How to solve $2e^3\cos (6z)-e^6=1$, being $z\in\mathbb{C}$.

Published on 15 Apr 2026 - 10:48

99

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Proof Check: Complex function and Branch points

Published on 10 May 2026 - 17:07

33

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finding locus of z using information about $z^2$

Published on 26 Mar 2026 - 4:51

177

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Evaluate $\frac{q}{1+q^2}+\frac{q^2}{1+q^4}+\frac{q^3}{1+q^6}$, where $q^7=1$ and $q\neq 1$.

Published on 16 Apr 2026 - 18:53

128

Views

Using Euler's Formula to prove $\sin^32x\cos^23x = -\frac1{16}(\sin12x-3\sin8x+2\sin6x+3\sin 4x-6\sin 2x) $

Published on 16 Apr 2026 - 10:58

158

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how can we find domain of analyticity of $f(z)$

Published on 13 Apr 2026 - 16:23

721

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Given a complex number $\omega=\cos(2\pi/5)+i\sin(2\pi/5)$

Published on 15 Apr 2026 - 23:46

534

Views

$\mathbb{C}$ is the smallest algebraically closed field containing $\mathbb{R}$

Published on 14 Apr 2026 - 11:25

List Question

if $\ Re(z)<0$ and $e^z=z+1$ the $z=?$

Find the polynomial $P(x)$ s.t. for any $a,b\in\Bbb C$ s.t. $a^2+b^2=ab$, $P(a+b)=6\big(P(a)+P(b)\big)+15a^2b^2(a+b)$.

Which complex numbers satisfy $(-1)^z=1$ and $(-1)^z=-1$?

Factoring $z^4+64=0$

Explaining why $i^n$ can only be equal to $1,i,-1,-i$

Set of points $\left| \frac{z+i\bar z}{2}\right|=\left| z-\frac{1+i}{2}\right|$

Integration - substitution that introduces $i$ into the integrand

How to solve $2e^3\cos (6z)-e^6=1$, being $z\in\mathbb{C}$.

Proof Check: Complex function and Branch points

finding locus of z using information about $z^2$

Evaluate $\frac{q}{1+q^2}+\frac{q^2}{1+q^4}+\frac{q^3}{1+q^6}$, where $q^7=1$ and $q\neq 1$.

Using Euler's Formula to prove $\sin^32x\cos^23x = -\frac1{16}(\sin12x-3\sin8x+2\sin6x+3\sin 4x-6\sin 2x) $

how can we find domain of analyticity of $f(z)$

Given a complex number $\omega=\cos(2\pi/5)+i\sin(2\pi/5)$

$\mathbb{C}$ is the smallest algebraically closed field containing $\mathbb{R}$

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