# THE MULTIPLICATIVE GROUP OF NON-ZERO COMPLEX NUMBERS

**Tutor description**

We will call a group that consists of a single element x ∈ G (called the group generator) a cyclic group generated by x and denoted by < x > if written in multiplication notation as G = < x > = {1, x, x 2 ,..........., x n −1} where x n = 1 . In particular, observe that the exponents of x include all negative integer as well as 0 and the positive integers ( x 0 is defined to be the identity). A finite *

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