Using the quadratic formula to solve for x^2:
x^2 = (1 +/- sqrt(1-4))/2
x^2 = (1 +/- sqrt(-3))/2
Using a calculator app that supports complex numbers shows numerically that the square roots of the two options are
sqrt(3)/2 + i/2
sqrt(3)/2 - i/2
so the four roots of the equation are the positive and negative of these two, with the other two then being
-sqrt(3)/2 - i/2
-sqrt(3)/2 + i/2
Of interest is that the real and imaginary parts have been interchanged in the square root process.
Using one of the solutions in the formula to be evaluated results in a number whose real and imaginary parts are on the order of 10^-16, close enough to call zero in this context.
Posted by Charlie
on 2016-11-14 12:41:24