Sifat Lapangan pada Bilangan Kompleks

Authors

  • Ida Nuraida UIN Sunan Gunung Djati

DOI:

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

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.

Author Biography

Ida Nuraida, UIN Sunan Gunung Djati

Pendidikan Matematika

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.

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Published

2017-06-05

Issue

Vol. 3 No. 1 (2017): Volume 3 Nomor 1 (2017)

Section

Articles

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