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## Main Question or Discussion Point

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?

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?