Question

How to study a function (e.g $\frac{e^x-e^{-x}}{2}$) whose $\{1,2\}$-th derivatives have complex solutions?

score 64 · Answer 1 · 2026-04-12 11:36:55

64

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How to study a function (e.g $\frac{e^x-e^{-x}}{2}$) whose $\{1,2\}$-th derivatives have complex solutions?

Published on 12 Apr 2026 - 11:36

score 290 · Answer 2 · 2026-04-14 23:48:10

290

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Does iterating the complex function $z\mapsto\frac{2\sqrt z}{1+z}$ always converge?

Published on 14 Apr 2026 - 23:48

score 121 · Answer 3 · 2026-05-16 01:14:33

121

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Can the function Re$(z^2)$ be approximated uniformly on the unit circle by rational functions having only simple poles?

Published on 16 May 2026 - 1:14

score 193 · Answer 4 · 2026-05-10 20:39:13

193

Views

If $(a+bi)$ is a unit in $\mathbb{Z} [i]$, then $N(a+bi) = 1$?

Published on 10 May 2026 - 20:39

score 281 · Answer 5 · 2026-04-16 23:51:40

281

Views

Why Zeros not isolated in $ \mathbb{R}$

Published on 16 Apr 2026 - 23:51

score 752 · Answer 6 · 2026-04-11 18:54:40

752

Views

Absolute value of the sum of two complex numbers squared

Published on 11 Apr 2026 - 18:54

score 85 · Answer 7 · 2026-04-13 20:50:55

85

Views

I've been having some trouble with a precalculus question. It's in the body.

Published on 13 Apr 2026 - 20:50

score 87 · Answer 8 · 2026-04-15 10:15:24

87

Views

Finding various things given Cos(a-b)+Cos(b-c)+Cos(c-a) = $\frac{-3}{2}$

Published on 15 Apr 2026 - 10:15

score 948 · Answer 9 · 2026-03-27 04:58:57

948

Views

How do I write the Laurent series for $\frac{1}{z^2(z-i)}$ for $1<|z-1|<\sqrt2$?

Published on 27 Mar 2026 - 4:58

score 102 · Answer 10 · 2026-04-14 16:00:33

102

Views

Solve Complex Equation $z^3 = 4\bar{z}$

Published on 14 Apr 2026 - 16:00

score 578 · Answer 11 · 2026-04-14 22:32:04

578

Views

Find an upper bound for a modulus of a complex number

Published on 14 Apr 2026 - 22:32

score 119 · Answer 12 · 2026-04-16 16:30:04

119

Views

For $n \in \Bbb{Z}_{>0}$, let $(3+i)^n = a_n+ib_n$, where $a_n, b_n \in \Bbb{Z}$.

Published on 16 Apr 2026 - 16:30

score 46 · Answer 13 · 2026-04-15 23:27:44

46

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Find real numbers r and s so that $a_{n+2}+ra_{n+1}+sa_n = 0$ and $b_{n+2}+rb_{n+1}+sb_n = 0$

Published on 15 Apr 2026 - 23:27

score 67 · Answer 14 · 2026-04-17 10:45:43

Why does that fact that $a_n \equiv 3 \pmod 5$ and $b_n\equiv 1 \pmod 5$ imply $1/\pi(\arctan(1/3))$ is irrational

score 86 · Answer 15 · 2026-04-13 20:28:12

86

Views

Why are radians treated like a quantity while degrees are treated like a unit?

Published on 13 Apr 2026 - 20:28

List Question

How to study a function (e.g $\frac{e^x-e^{-x}}{2}$) whose $\{1,2\}$-th derivatives have complex solutions?

Does iterating the complex function $z\mapsto\frac{2\sqrt z}{1+z}$ always converge?

Can the function Re$(z^2)$ be approximated uniformly on the unit circle by rational functions having only simple poles?

If $(a+bi)$ is a unit in $\mathbb{Z} [i]$, then $N(a+bi) = 1$?

Why Zeros not isolated in $ \mathbb{R}$

Absolute value of the sum of two complex numbers squared

I've been having some trouble with a precalculus question. It's in the body.

Finding various things given Cos(a-b)+Cos(b-c)+Cos(c-a) = $\frac{-3}{2}$

How do I write the Laurent series for $\frac{1}{z^2(z-i)}$ for $1<|z-1|<\sqrt2$?

Solve Complex Equation $z^3 = 4\bar{z}$

Find an upper bound for a modulus of a complex number

For $n \in \Bbb{Z}_{>0}$, let $(3+i)^n = a_n+ib_n$, where $a_n, b_n \in \Bbb{Z}$.

Find real numbers r and s so that $a_{n+2}+ra_{n+1}+sa_n = 0$ and $b_{n+2}+rb_{n+1}+sb_n = 0$

Why does that fact that $a_n \equiv 3 \pmod 5$ and $b_n\equiv 1 \pmod 5$ imply $1/\pi(\arctan(1/3))$ is irrational

Why are radians treated like a quantity while degrees are treated like a unit?

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