Euler’s Formula 3D Visualization — Manim Script .... تَصَوُّرٌ ثُلَاثِيُّ الأَبْعَادِ لِصِيغَةِ أُولِر مَشْهَدٌ ثُلَاثِيٌّ لِفَهْمِ الاِرْتِبَاطِ بَيْنَ الجُزْأَيْنِ الحَقِيقِيّ وَالتَّخَيُّلِيّ – رَسْمٌ مُتَحَرِّكٌ تَعْلِيمِيٌّ

This project provides a fully animated 3D visualization that illustrates how complex rotation behaves over time. A moving curve travels through three-dimensional space while its components are projected onto multiple planes, allowing the viewer to clearly see how the real and imaginary parts evolve. The scene includes smooth camera angles, shaded projection areas, dynamic color-coded traces, and highlighted points that follow the motion precisely. The code is fully commented in a tutorial‑friendly format, making it easy to customize or integrate into educational videos. This is an excellent tool for teachers, students, and content creators who want to explain advanced mathematical concepts through intuitive visual animation.