Imaginary Number Base

[Shadow]

Hey all,

 

base 2i can be quite interesting any poistive negative' date=' imagenary or negative imagenary number can be represented with out a special sign.

[/quote']

 

This is what bob000555 wrote in another topic of mine. I was just wondering if one can indeed have imaginary bases, and if so, how does one convert to/from them. And is what bob000555 says true?

 

Cheers,

 

Gabe

[ajb]

It is true. Not that I was aware of it before. Have a look at Wiki for a start.

[Shadow]

I did look, but I completely missed that page, so thanks for pointing it out.

 

Another question, it say that in base 2i one can represent every complex number using only the digits 0, 1, 2 and 3. What about irrational numbers, such as [math]\pi[/math] or [math]e[/math]?

 

Cheers,

 

Gabe

[Tom Vose]

Wow, didn't know that.

[bob000555]

I did look, but I completely missed that page, so thanks for pointing it out.

 

Another question, it say that in base 2i one can represent every complex number using only the digits 0, 1, 2 and 3. What about irrational numbers, such as [math]\pi[/math] or [math]e[/math]?

 

Cheers,

 

Gabe

 

Obviously you couldn’t represent them perfectly unless you had an infinite number of digit places. Just like in base ten as the number of places increases the accuracy with which you can represent the number increases.

 

There is really no magic to number systems, you could use absolutely anything as a base and the system will be defined as

 

[math]

\sum_{k=1}^n a_kb^k + \sum_{k=0}^{\infty}c_kb^{-k}

[/math]

Where a is the set of numbers before the decimal, c is the set of numbers after the decimal, b is base and n is the number of digits.

Edited December 21, 2008 by bob000555