i_ish.rb

# When Math.sqrt(2).fdiv(2) is just too zippy.

require 'bigdecimal'
require 'bigdecimal/util'

def i_ish(precision:)
  sqrt_2 = 2.to_d.sqrt precision
  sqrt_i = Complex sqrt_2 / 2, sqrt_2 / 2
  sqrt_i * sqrt_i
end

0.step do |n|
  imaginary = i_ish(precision: n).imaginary
  nines = imaginary.to_digits.delete_prefix('0.')[/\A9*/]
  puts "2.to_d.sqrt(#{n}) nines: #{nines.size}"
end