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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c924432-5356-4d2a-9799-f03f3a53c4ab%2F35df84c8-f4b2-4b96-8b71-cf3dc6cb0db3%2Fvbr8npr_processed.jpeg&w=3840&q=75)
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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