Numeric approximations to the imaginary number: the imaginary value

Part 1

With a number for -1, we can calculate the value of i.

In base 2, …111 =-1, so we need a number x such that x^2 = …111. We can multiply by term order to iteratively solve.

For the first term:

1 = x0*x0

So x0=1

Second term:

1 = x1*1 + 1*x1

1 = 2*x1

So x1 = 1/2

Third term:

1 = x2*1 + (1/2)*(1/2) + 1*x2

1 = 2*X2 + 1/4

3/4 = 2*X2

So x2 = 3/8

And so on. We now have a numeric representation of i in base 2.

… (35/128) (5/16) (3/8) (1/2) (1)

Next time we will investigate some properties of this number.