Get the solution to "In the froup Z12, find |a|, |b|, and..." - Plainmath

College
Algebra
Abstract algebra

necessaryh

Answered question

2021-01-15

In the froup

Z_{12}

, find |a|, |b|, and |a+b|
a=6, b=2

Answer & Explanation

tafzijdeq

Skilled2021-01-16Added 92 answers

Consider the provided qustion,
If a

\in Z_{n}

then

| a | = \frac{n}{gcd (a, n)}

here given

Z_{12}

. So, n=12
Given a = 6, b = 2
So, a + b = 6 + 2 = 8

| a | = | 6 | = \frac{12}{gcd (6, 12)} = \frac{12}{6} = 2

| b | = | 2 | = \frac{12}{gcd (2, 12)} = \frac{12}{2} = 6

| a + | = | 8 | = \frac{12}{gcd (8, 12)} = \frac{12}{4} = 3

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