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 2 is related to the property of silver ratios. if the square root symbol is interpreted suitably for the complex numbers and . for square roots and only one minus sign. Similar in appearance but with a finite number of terms, appears in various trigonometric constants: It is not known whether is a normal number, a stronger property than irrationality, but statistical analyses of its binary expansion are consistent with the hypothesis that it is normal to base two. The identity , along with the infinite product representations for the sine and cosine, leads to products such as and or equivalently,