Sifat Lapangan pada Bilangan Kompleks

Ida Nuraida

doi:10.15575/ja.v3i1.1498

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Sifat Lapangan pada Bilangan Kompleks

Ida Nuraida^(1*)

(1) UIN Sunan Gunung Djati, Indonesia
(*) Corresponding Author

Abstract

Dalam teori gelanggang dibahas sifat-sifat lapangan (field) pada suatu sistem bilangan. Suatu gelanggang komutatif L disebut lapangan jika untuk setiap a∈L dan a≠0 terdapat a^(-1)∈L, sehingga aa^(-1)=a^(-1) a=1. Diantaranya adalah sifat lapangan pada sistem bilangan kompleks. Bilangan kompleks adalah bilangan yang berbentuk a + bi atau a + ib, a dan b bilangan real dan i^2= –1. Notasi bilangan kompleks dinyatakan dengan huruf C. Dapat dibuktikan bahwa bilangan kompleks memiliki sifat-sifat lapangan yang memenuhi 10 sifat, yaitu sifat tertutup penjumlahan dan perkalian, komutatif penjumlahan dan perkalian, assosiatif penjumlahan dan perkalian, memiliki identitas penjumlahan dan perkalian, memiliki balikan (invers) penjumlahan dan balikan perkalian.

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References

Herstein, I.N. (1975). Topics in Algebra. 2¬^nd ¬ Ed. New York : John Wiley and Sons.

Gilbert, Jimmie & Gilbert, Linda. (2000). Elements of Modern Algebra. United Satates of America : Brooks/Cole.

Muchlis, Ahmad & Astuti, Pudji. (2007). Aljabar I. Jakarta : Universitas Terbuka.

DOI: https://doi.org/10.15575/ja.v3i1.1498

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