This may seem like a very elementary question...but here goes anyway.(adsbygoogle = window.adsbygoogle || []).push({});

When a positive number is raised to the power 1/2, I have always assumed that this is defined as the PRINCIPAL (positive) square root, e.g. [tex]7^{1/2} = \sqrt{7},[/tex]. That is, it does not include both the positive and negative square rootsL [tex]7^{1/2} \neq -\sqrt{7} = -7^{1/2}.[/tex]

In complex analysis, however, this doesn't seem to be the case? E.g. we write [tex](-1)^{1/2} = \pm i.[/tex]

Have I understood these conventions correctly? I have also been thinking about a similar situation: how in real analysis we think of every positive number as having a single natural logarithm, e.g. [tex]\ln 2 = 0.693\dotsc,[/tex] when in fact there are actually infinitely many:

[tex]\ln 2 = 0.693\dotsc + 2\pi n i \qquad (n=0,\pm1,\pm2,\dots).[/tex]

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

Join Physics Forums Today!

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

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

# Raising to half power = PRINCIPAL square root?

Loading...

Similar Threads - Raising half power | Date |
---|---|

I Constant raised to complex numbers | May 22, 2017 |

A Prove half step scheme is TVD | Jan 26, 2016 |

Roots of series of exponential raised to power of x? | Feb 19, 2015 |

Purpose of using 10^7 or any # raised | Dec 18, 2014 |

A Number Raised to the m Power | Feb 2, 2014 |

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