i
7
have equivalents in L2 . However, the same proof that
showed 2 doesn't exist also shows -1
doesn't exist.
If we try finding the square roots of -7 base 2, we get the following...
...0011100100110001100000010110101
...1100011011001110011111101001011
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.
...31141421404340423140223032431212
...13303023040104021304221412013233
Question: Given these pairs of square roots, how do you decide which is positive and which is negative?
© Scott Sherman 1999