Square root any nonnegative number, then the principal square root of −"x" is The right side (as well as its negative) is indeed a square root of −"x", since For every non-zero complex number "z" there exist precisely two numbers "w" such that : the principal square root of "z" (defined below), and its negative. There are two complex numbers that square to a given arbitrary non-zero imaginary number formula_11 with real formula_12 where the two-digit pattern {3, 6} repeats over and over again in the partial denominators. Since , the above is also identical to the following generalized continued fractions: The
Square root of numbers, called the complex numbers, that does contain solutions to the square root of a negative number. This is done by introducing a new number, denoted by "i" (sometimes "j", especially in the context of electricity where ""i"" traditionally represents electric current) and called the imaginary unit, which is "defined" such that . Using this notation, we can think of "i" as the square root of −1, but notice that we also have and so −"i" is also a square root of −1. By convention, the principal square root of −1 is "i", or more generally, if "x" is