Beyond the Number Line A Deep Geometric Understanding of Complex Numbers - Chapter 1 скачать в хорошем качестве

Beyond the Number Line A Deep Geometric Understanding of Complex Numbers - Chapter 1

This video rebuilds complex numbers from first principles by breaking the limitation of the number line and expanding mathematics into the complex plane. Starting with the unsolvable equation x² + 1 = 0, we introduce the imaginary unit i as a necessary mathematical expansion, not a fiction. You will see how complex numbers are structured as z = a + bi, how addition and multiplication follow strict algebraic rules, and why i cycles every four powers. The video then exposes the hidden geometry behind the algebra, showing complex numbers as points and vectors in a two-dimensional plane. Concepts such as conjugates, modulus, argument, and division are explained visually and logically. The journey concludes with polar form, revealing multiplication as rotation and scaling, and setting the foundation for Euler’s formula and De Moivre’s theorem. This is not memorization. This is structural understanding.