List questions from complex-numbers

Published on 02 Apr 2026 - 3:13

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How to find the number of non-negative/positive integer solutions to $m_1x_1+\cdots+m_rx_r=n$ systematically? (coin-exchange problem)

Published on 25 Mar 2026 - 20:36

1.1k

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Why does multiplication by purely imaginary numbers, regardless of magnitude, not cause purely rotation?

Published on 27 Mar 2026 - 3:44

1.4k

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Complex multi-valued function concept

Published on 16 Jun 2019 - 20:52

37

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Let $w \in G_{15}$ be a primitive root. Find every $n \in \mathbb{N}$ such that $\sum_{i=2}^{n-1} w^{3i} = 0$

Published on 25 Mar 2026 - 15:28

176

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Complex roots of unity: Proof

Published on 26 Mar 2026 - 19:25

96

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Proof using DMT and Binomial Expansion

Published on 17 Jun 2019 - 13:13

26

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Mappings between $\mathcal D(0,1)$ and $\mathbb{C}_+$: what's the difference?

Published on 27 Mar 2026 - 5:36

76

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Finding constant given there are no complex roots

Published on 08 Apr 2026 - 19:34

624

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Why isn't $\bar{z}$ differentiable?

Published on 18 Jun 2019 - 2:23

118

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For the equation $z^3 = \cos\theta + i\sin\theta = \mathop{\rm{cis}}\theta$, prove that the sum of the roots is always $0$

Published on 28 Mar 2026 - 9:28

438

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$\omega$ is a solution of $x^2+x+1=0$, find $\omega^{10}+\omega^5+3$

Published on 29 Mar 2026 - 20:17

284

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Calculating $\binom{n}{0}+\binom{n}{4}+\binom{n}{8}+\cdots$

Published on 30 Mar 2026 - 13:37

96

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Pell's equation solution set

Published on 26 Mar 2026 - 2:33

77

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Complex analysis principle branch logarithm

Published on 19 Jun 2019 - 11:26

List Question

Solve equation with exponential and sine.

How to find the number of non-negative/positive integer solutions to $m_1x_1+\cdots+m_rx_r=n$ systematically? (coin-exchange problem)

Why does multiplication by purely imaginary numbers, regardless of magnitude, not cause purely rotation?

Complex multi-valued function concept

Let $w \in G_{15}$ be a primitive root. Find every $n \in \mathbb{N}$ such that $\sum_{i=2}^{n-1} w^{3i} = 0$

Complex roots of unity: Proof

Proof using DMT and Binomial Expansion

Mappings between $\mathcal D(0,1)$ and $\mathbb{C}_+$: what's the difference?

Finding constant given there are no complex roots

Why isn't $\bar{z}$ differentiable?

For the equation $z^3 = \cos\theta + i\sin\theta = \mathop{\rm{cis}}\theta$, prove that the sum of the roots is always $0$

$\omega$ is a solution of $x^2+x+1=0$, find $\omega^{10}+\omega^5+3$

Calculating $\binom{n}{0}+\binom{n}{4}+\binom{n}{8}+\cdots$

Pell's equation solution set

Complex analysis principle branch logarithm

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