Analisis Sifat-Sifat Transformasi Mobius pada Fungsi Kompleks - Mubarok, Faris; Gani Gunawan (UPT Publikasi Ilmiah Unisba, 2025)
Abstract. This journal discusses the properties of the Mobius Transformation based on geometric aspects and algebraic structure. Namely, in the geometric aspect, the Mobius Transformation can be viewed as four compositions that were previously considered as two compositions. The research results show that the Mobius Transformation can be viewed as four compositions with three geometric transformations, namely dilation, rotation, translation, and one inversion. In the aspect of algebraic structure, the Mobius Transformation satisfies the group property under function composition and can be represented in a 2x2 matrix that has isomorphic properties based on bijective and homomorphic properties, which preserve its operation and functional structure. Thus, it can be concluded that the Möbius Transformation has bijective properties, can be viewed with four compositions, has group properties, and is isomorphic. Abstrak. Artikel ini membahas sifat-sifat dari Transformasi Mobius (TM) berdasarkan aspek geometri dan struktur aljabar. Dalam aspek geometri, TM dapat dipandang sebagai transformasi dengan empat komposisi yang sebelumnya dipandang sebagai dua komposisi. Hasil penelitian menunjukkan bahwa komposisi geometri pada transformasi mobius merupakan transformasi geometri dilatasi, rotasi, translasi dan satu inversi. Pada aspek struktur aljabar, TM memenuhi sifat grup di bawah fungsi komposisi, dan dapat direpresentasikan dalam matriks dua kali dua yang memiliki sifat isomorfik berdasarkan sifat bijektif dan homomorfisma yaitu mempertahankan operasi dan struktur fungsinya.