Given integer n>0 let G ne the subset of complex numbersof the form e^((2kpii/n)i), k is an element of Z . Show that G is a group under multiplication.Howmany elements does G have?
Given integer n>0 let G ne the subset of complex numbersof the form e^((2kpii/n)i), k is an element of Z . Show that G is a group under multiplication.Howmany elements does G have?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Given integer n>0 let G ne the subset of complex numbersof the form e^((2kpii/n)i), k is an element of Z . Show that G is a group under multiplication.Howmany elements does G have?
Expert Solution
Step 1
Note:- A set G is called Group with respect to a binary operation say if
1. G is closed.
2. G is associative.
3. G has an identity element.
4. G has an inverse element.
Given information
G is the subset of complex numbers of the form .
Here, .
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