Complex Numbers in Leftins

If we try finding the square roots of -7 base 2, we get the following...


Thus the imaginary numbers i7 have equivalents in L2 . However, the same proof that showed 2 doesn't exist also shows -1 doesn't exist.

So, similar to the results with irrationals, we find that some complex numbers, such as 1/8 + i7, exist, but some, such as i, don't.

     C Lf .
     C Lf .

One interesting thing to note is that base 5 is the first base that can represent -1. They look like irrational numbers.


    Question: Given these pairs of square roots, how do you decide which is positive and which is negative?

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© Scott Sherman 1999