To perform: The operation [-3][9] in Z_{15} and indicate the answer in [r] where 0\leq r\leq m.

Carol Gates

Carol Gates

Answered question

2021-04-24

To perform: The operation [-3][9] in Z15 and indicate the answer in [r] where 0rm.

Answer & Explanation

Ezra Herbert

Ezra Herbert

Skilled2021-04-26Added 99 answers

Procedure used:
Procedure to perform operation in Zm.
1 Consider the operation.
2 Perform the operation with the help of congruence.
3 Obtain and dictate the answer.
Viability of congruence.
The congruence defined as x=y(bmodm) is true if x - y is divisible by m.
Calculation:
Consider the given operation [-3] [9].
It is evident that [x][y] = [xy].
[-3][9]=[-3*9]=[-27]
Therefore, in Z15 the above operation can be written as shown below:
[-3][9] =[-27]
=[3]   [273(bmod15)]
Since r=0([r] where 0r15).
Therefore, the operation [-3][9] in Z15 will result as [-3][9]=[3].

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