THE SQUARED ABSOLUTE VALUE OF (a +bi)+ (c +di)^(1/2^n )

Abstract

The squared absolute value of A = (a + bi +(c +di)^0,5) can be expressed simply by AA = (a + bi +(c +di)^0,5)(a - bi +(c -di)^0,5), so by roots of complex numbers. Because this expression is real we are interested in an expression, if it exists, that uses only square roots of positive numbers. This expression with only roots of positive numbers is also given for the more general case with  with 2^n-th roots.