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Let H = {a+bila,bE3Z}. group (a) Show that H is a subgroup of C, the complex numbers under addition. (b) Give an example of a nontrivial, proper subgroup K in H

Let H = {a+bila,bE3Z}. group (a) Show that H is a subgroup of C, the complex numbers under addition. (b) Give an example of a nontrivial, proper subgroup K in H

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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Let \( H = \{ a + bi \mid a, b \in 3\mathbb{Z} \} \). **(a)** Show that \( H \) is a subgroup of \( \mathbb{C} \), the complex numbers under addition. **(b)** Give an example of a nontrivial, proper subgroup \( K \) in \( H \).
Transcribed Image Text:Let \( H = \{ a + bi \mid a, b \in 3\mathbb{Z} \} \). **(a)** Show that \( H \) is a subgroup of \( \mathbb{C} \), the complex numbers under addition. **(b)** Give an example of a nontrivial, proper subgroup \( K \) in \( H \).
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