Let Wn be the complex n'th roots of unity, with the operation of complex multiplication. We have shown that Wn is a group. a) Show that Wnis cyclic. b) Find all generators of Wn. Explain your answer

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.2: Ring Homomorphisms
Problem 15E: In the field of a complex numbers, show that the mapping that maps each complex number onto its...
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Let Wn be the complex n'th roots of unity, with the operation of complex multiplication.
We have shown that Wn is a group.
a) Show that Wn is cyclic.
b) Find all generators of Wn. Explain your answer
Transcribed Image Text:Let Wn be the complex n'th roots of unity, with the operation of complex multiplication. We have shown that Wn is a group. a) Show that Wn is cyclic. b) Find all generators of Wn. Explain your answer
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