consider the two vectors v1 = (3i, 2), v2 = (-3, 2i). in C^2 Above C we get, v1 * i = v2, therefore they are dependent. Now above R, we can't see that they are dependent. Why if i take the determinant of those vectors i get get 0 |v1 v2| = 2x2 matrix = 0 ( which means two column vectors are independent). Does the determinant works only above C in this case because above R they are independent and yet we get same result of the determinant?