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karnten07

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**[SOLVED] Complex numbers as an abelian group**

## Homework Statement

Multiplication of complex numbers defines a binary operation on C^x:=C\{0} (complex numbers not including zero). Show that C^x together with this binary operation is an abelian group. (without further discussion you may use the usual laws of algebra for R,

such as associativity for addition and multiplication of real numbers)

p.s the wording may sound strange because my lecturer is european i think and english is his second language.

## Homework Equations

## The Attempt at a Solution

I know that for an abelian it must show commutativity, ie, x*y=y*x. For it to be a group there must be associativity of multiplication, that en element exists e, that is an identity element ie. e*x=x and x*e=x, and also that there is an element y, that is an inverse element ie. x*y=e and y*x=e

I have wrote this information out in my answer but i think i might need to show it in an example. What kind of example would someone suggest, maybe (1+i) x (1-i). Giving 1 +1=2?? Any ideas guys? Thanks