Proving the Group Properties of M, the Set of Nth Roots of Unity

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SUMMARY

The discussion centers on proving that the set M, defined as M = {e^(j*2*pi*k/n) | k = 0, 1, 2, ..., n-1}, which represents the nth roots of unity, forms a group under the operation of complex number multiplication. To establish this, one must demonstrate four key properties: closure, associativity, the existence of an identity element, and the existence of inverses. Participants seek clarification on these properties and their application to the set M.

PREREQUISITES
  • Understanding of complex numbers and their multiplication
  • Familiarity with the concept of groups in abstract algebra
  • Knowledge of the nth roots of unity and their mathematical representation
  • Basic principles of mathematical proof techniques
NEXT STEPS
  • Study the properties of groups in abstract algebra
  • Learn about the closure property in the context of complex number operations
  • Explore the concept of identity elements and inverses in group theory
  • Investigate examples of other sets that form groups under multiplication
USEFUL FOR

Mathematics students, educators, and anyone interested in abstract algebra, particularly those studying group theory and complex numbers.

ustus
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Hello,
Please help in solving the four set of problems, i will be very happy explaining comment as really want to understand.
The problem will spread to the extent of understanding preduduschey.

1 Problems:

The set M, M = {e^(j*2*pi*k/n) , k= 0,1,2...n-1} denotes the set of the nth roots of unity,
i.e. the solution set of z^n = 1 for fixed n.
Show that M, together with multiplication of complex numbers, forms a group.
 
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ustus said:
Hello,
Please help in solving the four set of problems, i will be very happy explaining comment as really want to understand.
The problem will spread to the extent of understanding preduduschey.

1 Problems:

The set M, M = {e^(j*2*pi*k/n) , k= 0,1,2...n-1} denotes the set of the nth roots of unity,
i.e. the solution set of z^n = 1 for fixed n.
Show that M, together with multiplication of complex numbers, forms a group.

Ok. To show something is a group, what four things do you need to show?

Which one(s) are you stuck on?
 
Are the following evidence to the problem?
 

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