Question

find the squaer root of 6+8i

Answer 1

it will be equal to (6+8i)^1/2

Answer 2

Let        z2 = (x + yi)2  = 8 – 6i

             (x2 – y2) + 2xyi     = 8 – 6i

         Compare real parts and imaginary parts,

                                         x2 – y2 = 8

                                         2xy = -6

         Now, consider the modulus:         |z|2 = |z2|

                             x2 + y2 = Ö(82 + 62) = 10

         Solving (1) and (3), we get           x2 = 9   and    y2 = 1

                                                                 x = ±3  and          y = ±1

         From (2), x and y are of opposite sign,

                  (x = 3 and y = -1)    or   (x = -3 or y = 1)

                  z =  ± (3 – i)

Hope it is helpful