Quote:

Show that the set G = {1,-1,i,-i} (i - (sqrt of -1))

forms a group with respect to multiplication of complex numbers.Obtain a non trivial subgroup h, justifying your choice and use it to illustrate Lagranges Theorem

With equal ease show that $\displaystyle \mathcal{Z}_n=\left\{z\in\mathbb{C}:z^n=1\right\}$ is a group (looking at it like that is even easier). If this group were to have a group it would have to be a divisor of $\displaystyle 4$ and thus is either $\displaystyle 1,2,4$...but since the subgroup a non-trivial (assumed proper) it must be $\displaystyle 2$...finish it.