I think a lot a users have vague concepts about the roots of unity.(adsbygoogle = window.adsbygoogle || []).push({});

I try to post a link to WolframAlpha, which calculates all the second roots

of unity

http://www.wolframalpha.com/input/?i=sqrt(1)

There you can see the input [itex]\sqrt{1}[/itex] and the plot of all roots in the complex

plane.

The roots are lying on the unit circle [itex]\ e^{i\alpha}[/itex] = cos[itex]\alpha[/itex]+i[itex]\dot{}[/itex]sin[itex]\alpha[/itex]

There are two real roots as you can see on the plot:

[itex]\sqrt{1}[/itex] = +1 (principal root)

[itex]\sqrt{1}[/itex] = -1

Wikipedia says that there exists a mathematical fallacy of the following kind:

1= [itex]\sqrt{1}[/itex] = [itex]\sqrt{(-1)\dot{}(-1)}[/itex] = [itex]\sqrt{-1}[/itex][itex]\dot{}[/itex][itex]\sqrt{-1}[/itex] = i[itex]\dot{}[/itex]i = -1

the fallacy is that the rule [itex]\sqrt{x\dot{}y}[/itex] = [itex]\sqrt{x}[/itex][itex]\dot{}[/itex][itex]\sqrt{y}[/itex] is not valid here according to Wikipedia:

http://en.wikipedia.org/wiki/Mathematical_fallacy#Positive_and_negative_roots

WolframAlpha implies no error. Which one should we trust? My guess is

Wikipedia is just wrong and WolframAlpha is correct.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Wolfram Alpha: all 2nd roots of 1

Loading...

Similar Threads - Wolfram Alpha roots | Date |
---|---|

I Problems with wolfram alpha | Sep 30, 2016 |

B Programs like Wolfram but offline | Jul 5, 2016 |

Horizontal tangent to wolfram alpha's heart-shaped graph | Dec 30, 2015 |

Wolfram alpha -- worth it for a beginner to get a wolfram alpha pro acct? | Jan 29, 2015 |

Am I correct or is Wolfram correct? | Jan 25, 2013 |

**Physics Forums - The Fusion of Science and Community**