Question

Why do we have to specifically define a branch of the complex square root function?

score 55 · Answer 1 · 2019-09-12 19:07:32

55

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Why do we have to specifically define a branch of the complex square root function?

Published on 12 Sep 2019 - 19:07

score 326 · Answer 2 · 2026-03-26 17:52:35

326

Views

Finding all the complex roots of $x^3 - x^2 + 1 = 0$

Published on 26 Mar 2026 - 17:52

score 247 · Answer 3 · 2019-09-14 20:35:24

247

Views

For integer $n>1$, can $\sum_{k=1}^{n}\sqrt{k}$ be a rational number? Can it be an integer?

Published on 14 Sep 2019 - 20:35

score 38 · Answer 4 · 2019-09-14 20:48:21

38

Views

comparing small sums of radicals

Published on 14 Sep 2019 - 20:48

score 75 · Answer 5 · 2019-09-14 21:27:25

75

Views

What is $(\sqrt3-1)^2$?

Published on 14 Sep 2019 - 21:27

score 66 · Answer 6 · 2019-09-15 01:04:52

66

Views

Help solve this equation: $\sqrt{3x-4}+\sqrt[3]{5-3x}=1$

Published on 15 Sep 2019 - 1:04

score 30 · Answer 7 · 2019-09-15 09:57:34

30

Views

Find the radical of${\langle x^2-y^2,x^4-x^2y^5\rangle}\subset \mathbb{C}[x,y]$

Published on 15 Sep 2019 - 9:57

score 263 · Answer 8 · 2019-09-15 11:06:30

263

Views

Prove $\lceil(3 + \sqrt{5})^n\rceil$ is divisible by $2^n$ for all natural numbers $n$

Published on 15 Sep 2019 - 11:06

score 79 · Answer 9 · 2026-02-23 03:31:11

79

Views

The real numbers $a,b,c,d$ satisfy $a^2+b^2+c^2+1=d+\sqrt{a+b+c-d}$. Find the value of $d$.

Published on 23 Feb 2026 - 3:31

score 171 · Answer 10 · 2019-09-16 19:16:47

171

Views

How to simplify this cube root in denominator expression?

Published on 16 Sep 2019 - 19:16

score 845 · Answer 11 · 2019-09-17 17:10:31

845

Views

Why is the range of radical functions all non-negative real numbers?

Published on 17 Sep 2019 - 17:10

score 135 · Answer 12 · 2019-09-17 20:03:50

135

Views

Solution to this radical equation?

Published on 17 Sep 2019 - 20:03

score 26 · Answer 13 · 2019-09-18 08:12:23

26

Views

Simple Harmonic Motion $\omega$'s sign concern

Published on 18 Sep 2019 - 8:12

score 349 · Answer 14 · 2019-09-18 13:23:28

349

Views

Solving a cube root with complex numbers

Published on 18 Sep 2019 - 13:23

score 332 · Answer 15 · 2019-09-21 15:55:56

332

Views

Prove that $\lim_{x\to\infty}\left\{\sqrt{ax^2 + bx + c} -\sqrt{px^2 + qx + r}~\right\}=\frac{b-q}{2\sqrt a}$

Published on 21 Sep 2019 - 15:55

List Question

Why do we have to specifically define a branch of the complex square root function?

Finding all the complex roots of $x^3 - x^2 + 1 = 0$

For integer $n>1$, can $\sum_{k=1}^{n}\sqrt{k}$ be a rational number? Can it be an integer?

comparing small sums of radicals

What is $(\sqrt3-1)^2$?

Help solve this equation: $\sqrt{3x-4}+\sqrt[3]{5-3x}=1$

Find the radical of${\langle x^2-y^2,x^4-x^2y^5\rangle}\subset \mathbb{C}[x,y]$

Prove $\lceil(3 + \sqrt{5})^n\rceil$ is divisible by $2^n$ for all natural numbers $n$

The real numbers $a,b,c,d$ satisfy $a^2+b^2+c^2+1=d+\sqrt{a+b+c-d}$. Find the value of $d$.

How to simplify this cube root in denominator expression?

Why is the range of radical functions all non-negative real numbers?

Solution to this radical equation?

Simple Harmonic Motion $\omega$'s sign concern

Solving a cube root with complex numbers

Prove that $\lim_{x\to\infty}\left\{\sqrt{ax^2 + bx + c} -\sqrt{px^2 + qx + r}~\right\}=\frac{b-q}{2\sqrt a}$

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