### Complex Numbers in Leftins

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 *L*^{2} . 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* *L*_{f}
.

*C* *L*_{f} .

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?

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© Scott Sherman 1999