Square Root of Complex Number

As before, r = sqrt(a * a + b * b)

sqrt(a + J*b)
 = sqrt(r) * (sqrt((1 + a / r) / 2) (+ or -) J * sqrt((1 - a / r) / 2))
 = sqrt((r + a) / 2) (+ or -) J * sqrt((r - a) / 2)
 = sqrt((sqrt(a * a + b * b) + a) / 2) (+ or -) J * sqrt((sqrt(a * a + b * b) - a) / 2)

caution ! (+ or -) should be chosen to be the same as the sign of b

example:

sqrt(3 - J * 2) = sqrt((sqrt(3 * 3 + 2 *2) + 3) / 2) - J * sqrt((sqrt(3 * 3 + 2 * 2) - 3) / 2)