Find the order of every element of the group (G,o), where G = {1,-1,i,-i}

Find the order of every element of the group (G,o), where G = {1,-1,i,-i}

Ans.

G={1,-1,i,-i}

    Here, '1' is the identity element i.e. of order 1

Also,

        (-1)² = (-1).(-1) = 1  i.e. '-1' is of order 2.

        (i)⁴ = (i.i.i.i) = 1  i.e. 'i' is of order 4.

And   (-i)⁴ = (-i).(-i).(-i).(-i) = 1  i.e '-i' is of order 4.