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 a 2 by 2 matrix If "B" is zero but "A" and "D" are not both zero, one can use This formula will provide two solutions if "A" = "D" or "A" = 0 or "D" = 0, and four otherwise. A similar formula can be used when "C" is zero but "A" and "D" are not both zero. Square root of a 2 by 2 matrix A square root of a 2×2 matrix "M" is another 2 by 2 matrix "R" such that "M" = "R", where "R" stands for the matrix product of "R" with itself. In general there can be no, two,