I've been doing a lot of thinking about imaginary numbers lately. My first question was "What is sqr(i)?".(adsbygoogle = window.adsbygoogle || []).push({});

I thought it was unsolvable until I punched it into my trusty (and often right) caclulator and found out it was (sqr(.5)i + sqr(.5))^2

So obvious now. Of course.

Anyways, a while later, I thought about series of powers (the same way a power is a series of multiplications and those a series of additions). (We'll call a series of power ^^)

So my question is:

x^^2 = x^x = -4

What is x?

My calculator tells me: false. But I have this tendency not to trust it sometimes, especially when it won't give me an answer.

Also, is i ^ i defined? ((-1)^.5)^((-1)^.5) = (-1)^(i/2) = ?

**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!

# Imaginary Numbers

Loading...

Similar Threads - Imaginary Numbers | Date |
---|---|

B Complex numbers imaginary part | Aug 28, 2017 |

B Is infinity an imaginary number? | Mar 4, 2017 |

B Simplifying roots of negative numbers | Feb 26, 2017 |

I Determining graphical set of solutions for complex numbers | Jan 4, 2017 |

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