HIMPUNAN BILANGAN KOMPLEKS YANG MEMBENTUK GRUP
DOI:
https://doi.org/10.24252/msa.v2i2.37322Keywords:
Bilangan kompleks, grup dan sifat-sifat grupAbstract
Bilangan riil banyak digunakan dalam menyelesaikan pembuktian sifat-sifat grup. Kemudian sifat-sifat grup tersebut akan dikaji dengan menggunakan himpunan bilangan kompleks. Tujuan dari penelitian ini adalah untuk mengetahui himpunan bilangan kompleks yang dapat membentuk grup atau bukan grup. Jenis penelitian yang digunakan dalam penelitian ini adalah penelitian murni (kajian teori). Hasil penelitian yang diperoleh adalah himpunan bilangan kompleks yang dapat membentuk grup dapat dilihat pada bentuk atau operasi tertentu yaitu penjumlahan dan perkalian bilangan kompleks dapat membentuk grup misalnya pada ℂ={?|?=?+??;?,?∈ℝ,?2=−1} dengan operasi (ℂ,+) dan (ℂ,×),ℂ={?̅|?=?+??;?,?∈ℝ,?2=−1} dengan operasi penjumlahan dan perkalian konjugat, ℂ={|?| |?=?+??; ?,?∈ℝ,?2=−1} dengan operasi perkalian modulo, ℂ={1?| ?=?+??;?,? ∈ℝ,?2=−1} dengan operasi (ℂ,+) dan (ℂ,×), ℂ={?|?=?+??√2 ;?,?∈ℝ,?2=−1} dengan operasi penjumlahan, ℂ={?|?=?+??;|?+??|=1;?,?∈ℝ,?2=−1} dengan operasi perkalian.
References
Departemen Agama Al-Quran dan terjemahannya. Bandung:PT.Syaamil Cipta Media:2005
Departemen Agama, Al-quran dan Terjemahannya. Jakarta: CV. Darus Sunnah 2002
Durbin,johnR, Introduction To Modern Algebra.http://roymahmud.wordpress.com/2009/06/29/aplikasi-group-dalam-bidang kristalografi/diakses pada tanggal1 desember 2013
Hendrijanto, Diktat kuliah struktur aljabar 1 (teori grup). Madiun: institut keguruan dan ilmu pendidikan, 2011
Ilham, Arifin. Bilangan Kompleks. Jakarta Selatan:Universita Indraprasta PGRI, 2001
Masyhuri, dkk, Metodologi Penelitian Pendekatan Praktis dan Aplikatif. Bandung:PT Refika Aditama. 2008
Noeyanti, Logika Matematika, Yogyakarta, http://www.docdatabase.net/details-teori-himpunan-logika-matematika-1073843.html
Prasetyono, Sunar, Dwi, dkk. Panduan Efektif Belajar Cepat Matematika Yogyakarta:Power Books (Ihdina). 2009
Rahman ,Abdul. Fungsi dengan Peubah Kompleks. Makassar:Universitas Negeri Makassar, 2002
Shihab, M. Quraish, Tafsir Al-Mishbah. Jakarta:Lentera Hati. 2007
SJ, Susilo, Frans. Himpunan dan Logika Kabur serta Aplikasinya. Yogyakarta:Graha Ilmu. 2006
Tahmir, Suradi. Teori Grup. Makassar:Andira Publisher. 2004
Tiro, M. Arif ,dkk. Teori Bilangan. Makassar:Andira Publisher. 2008
Tiro, M. Arif, dkk. Teori Peluang. Makassar: Andira Publiser. 2008
Tiro, M. Arif. Dasar-Dasar Statistik. Makassar:Andira Publisher, 2008
Downloads
Published
How to Cite
Issue
Section
License
Copyright Notice
Jurnal MSA (Matematika dan Statistika serta Aplikasinya)
Authors who publish in Jurnal MSA agree to the following copyright and licensing terms.
1. Copyright Ownership
Authors retain copyright in their scholarly articles unless copyright is lawfully held by another authorized rights holder.
Publication in Jurnal MSA does not require an exclusive transfer or assignment of copyright ownership to the journal or its publisher.
2. Non-Exclusive Publishing Rights
Authors or authorized copyright holders grant Jurnal MSA non-exclusive rights of first journal publication, dissemination, indexing, and digital preservation.
These rights allow the journal to publish, reproduce, distribute, archive, and preserve the accepted scholarly article without transferring copyright ownership.
3. Publication License
Jurnal MSA adopts and applies the Creative Commons Attribution 4.0 International License (CC BY 4.0) as the standard license for scholarly articles published under its current publication terms.
Authors or authorized rights holders authorize publication of their articles under CC BY 4.0.
This license permits sharing, reproduction, redistribution, adaptation, and reuse, including commercial reuse, subject to the license terms and attribution requirements.
Official License:
https://creativecommons.org/licenses/by/4.0/
4. Non-Commercial Publishing Model
Jurnal MSA operates as a non-commercial scholarly publisher dedicated to education, scientific research, and scholarly communication.
The journal's non-commercial status does not restrict commercial reuse of articles licensed under CC BY 4.0.
5. Authors' Rights and Self-Archiving
Authors retain their applicable rights to reuse, share, and disseminate their scholarly works.
Authors may immediately deposit and distribute the published version of their CC BY 4.0-licensed articles through institutional repositories, disciplinary repositories, and academic websites without an embargo imposed by the journal.
Such distribution remains subject to the applicable license and third-party rights.
6. Author Consent and Third-Party Rights
By agreeing to publication, the corresponding author confirms that:
-
All listed authors have approved the manuscript and the publication arrangements.
-
The authors or authorized rights holders possess the legal authority necessary to authorize publication and licensing.
-
Jurnal MSA is granted the necessary non-exclusive publishing rights.
-
Publication of the article under CC BY 4.0 is authorized.
-
Required permissions for third-party materials have been obtained, and any licensing exclusions have been clearly identified.
7. Previously Published Articles
Articles published before the implementation of the current licensing policy remain governed by their validly applicable copyright and licensing arrangements.
The adoption of CC BY 4.0 does not automatically change licenses previously granted under different terms.
Copyright and License Statement
Copyright © [Year], The Author(s).
The author(s) retain copyright and grant Jurnal MSA non-exclusive rights of first publication, dissemination, indexing, and preservation.
This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
