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Consider the set C4 = {i, -1, -i, 1}, the fourth roots of unity in the complex numbers. (a) Make a Cayley table for (C4,), the set C4 under the operation of complex multiplication. (b) Make a Cayley table for the set Z4 under addition of integers modulo 4. (c) Can one define a bijective map between (Z4, +) and (C4, ) such that the bijection will pro- duce a matching of the two tables? If so what is the bijection. If not, explain why.

Consider the set C4 = {i, -1, -i, 1}, the fourth roots of unity in the complex numbers. (a) Make a Cayley table for (C4,), the set C4 under the operation of complex multiplication. (b) Make a Cayley table for the set Z4 under addition of integers modulo 4. (c) Can one define a bijective map between (Z4, +) and (C4, ) such that the bijection will pro- duce a matching of the two tables? If so what is the bijection. If not, explain why.

Advanced Engineering Mathematics
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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8. Consider the set C4 = {i,-1, -i, 1}, the fourth roots of unity in the complex numbers. (a) Make a Cayley table for (C4,), the set C4 under the operation of complex multiplication. (b) Make a Cayley table for the set Z4 under addition of integers modulo 4. (c) Can one define a bijective map between (Z4, +) and (C4, ) such that the bijection will pro- duce a matching of the two tables? If so what is the bijection. If not, explain why.
Transcribed Image Text:8. Consider the set C4 = {i,-1, -i, 1}, the fourth roots of unity in the complex numbers. (a) Make a Cayley table for (C4,), the set C4 under the operation of complex multiplication. (b) Make a Cayley table for the set Z4 under addition of integers modulo 4. (c) Can one define a bijective map between (Z4, +) and (C4, ) such that the bijection will pro- duce a matching of the two tables? If so what is the bijection. If not, explain why.
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