Explained: "In the froup Z12, find |a|,|b|, and |a+b|..."

College
Algebra
Abstract algebra

necessaryh

Answered question

2021-02-27

In the froup $Z_{12}$ , find $| a |, | b |$ , and $| a + b |$
$a = 5, b = 4$

Answer & Explanation

Pohanginah

Skilled2021-02-28Added 96 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 $a = 5, b = 4$
So, $a + b = 5 + 4 = 9$
$| a | = | 5 | = \frac{12}{gcd (5, 12)} = \frac{12}{1} = 12$
$| b | = | 4 | = \frac{12}{gcd (4, 12)} = \frac{12}{4} = 3$
$| a + b | = | 11 | = \frac{12}{gcd (9, 12)} = \frac{12}{3} = 4$

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