recall that the order of an element of a group , is the smallest positive integer such that , where is the identity element of .

Hopefully you know how to interpret . it is just applying the operation of to times.

So, for example, for 3(i)(a). The element is in , which is the group of non-zero complex numbers with the operation multiplication.

Notice that , and 8 is the smallest positive integer power for which this happens (keep multiplying by itself until you get to 1, you'll notice you had to do this 8 times). hence, the order of is 8. the others are similar. (i'd probably use the cis notation for the complex number problems. or try to employ any other trick you know that allows you to multiply quickly).