Which of the following is a solution of x2 + 2x + 4? −2 + two i times the square root of 3 2 + two i times the square root of 3 1 − i times the square root of 3 −1 + i times the square root of 3

Strictly speaking, x^2 + 2x + 4 doesn't have solutions; if you want solutions, you must equate x^2 + 2x + 4 to zero:

x^2 + 2x + 4= 0.  "Completing the square" seems to be the easiest way to go here:

rewrite   x^2 + 2x + 4  as   x^2 + 2x + 1^2 - 1^2 = -4, or
                                              (x+1)^2 = -3
or                                            x+1 =i*(plus or minus sqrt(3))

or                                            x = -1 plus or minus i*sqrt(3)

This problem, like any other quadratic equation, has two roots.  Note that the fourth possible answer constitutes one part of the two part solution found above.