Find the quadratic equation whose roots are 3+- i / 2

(x - root#1) times (x - root#2) = 0 . . . . . This is how to BUILD the quadratic equation.

All the rest is just multiplying out that first line:

(x- (3+i/2)) times (x - (3-i/2)) = 0

x² -x(3-i/2) -x(3+i/2) + (3+i/2)(3-i/2) = 0

x² -3x + ix/2 -3x - ix/2 + 9 -3i/2 + 3i/2 = 0

x² -6x +9 = 0  There it is.  That's your quadratic equation.

The answer is the third choice