List questions from complex-numbers

Published on 13 Apr 2026 - 8:27

168

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If $z = \frac{(\sqrt{3} + i)^n}{(\sqrt{3}-i)^m}$, find the relation between $m$ and $n$ such that $z$ is a real number.

Published on 15 Apr 2026 - 20:16

48

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Quick trivial trigonometry question for polar form complex number

Published on 11 Apr 2026 - 23:14

122

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Polar complex form and exponent question

Published on 11 Apr 2026 - 11:35

61

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Complex numbered equation

Published on 11 Apr 2026 - 2:10

175

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Prove that $\not \exists$ $n \in \mathbb N\setminus \{0\}$ such that $(2+i)^n=(2-i)^n$

Published on 15 Apr 2026 - 23:32

48

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$f :\mathbb{D}\rightarrow \mathbb{D}$ is a holomorphic function and $z_0$ is a root of it, How can I prove $|z_0| \geq |f(0)|$

Published on 27 Mar 2026 - 14:59

50

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How to prove that my generalisation is true?

Published on 11 Apr 2026 - 21:18

127

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Study the complex number $z = \left( \frac{\sqrt{3} - i}{1 + i} \right) ^ {12}$.

Published on 16 Apr 2026 - 4:29

124

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Cauchy’s integral theorem statement

Published on 12 Apr 2026 - 23:48

165

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A corollary of Cauchy integral theorem

Published on 13 Apr 2026 - 3:54

48

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Why we rationalize, conjugate.

Published on 09 Apr 2026 - 20:43

88

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$(a^n-b^n)$ bounded implies $a=b$.

Published on 16 Apr 2026 - 8:24

52

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What I am missing here?

Published on 12 Apr 2026 - 11:47

109

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Is the standard definition of $i$ enough to uniquely describe it?

Published on 09 Apr 2026 - 10:30

List Question

Condition for $z$ to $|P(z)|\lt 1$

If $z = \frac{(\sqrt{3} + i)^n}{(\sqrt{3}-i)^m}$, find the relation between $m$ and $n$ such that $z$ is a real number.

Quick trivial trigonometry question for polar form complex number

Polar complex form and exponent question

Complex numbered equation

Prove that $\not \exists$ $n \in \mathbb N\setminus \{0\}$ such that $(2+i)^n=(2-i)^n$

$f :\mathbb{D}\rightarrow \mathbb{D}$ is a holomorphic function and $z_0$ is a root of it, How can I prove $|z_0| \geq |f(0)|$

How to prove that my generalisation is true?

Study the complex number $z = \left( \frac{\sqrt{3} - i}{1 + i} \right) ^ {12}$.

Cauchy’s integral theorem statement

A corollary of Cauchy integral theorem

Why we rationalize, conjugate.

$(a^n-b^n)$ bounded implies $a=b$.

What I am missing here?

Is the standard definition of $i$ enough to uniquely describe it?

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