Why Are There No 3 Dimensional "Complex Numbers"?

Explore the mathematical reasoning behind the absence of three-dimensional "complex numbers" in this 37-minute video lecture. Delve into the fundamental concepts of complex number systems and understand why their extension to three dimensions is not possible. Learn about the historical attempts to create higher-dimensional number systems and the mathematical limitations that prevent the existence of a three-dimensional analog to complex numbers. Gain insights into alternative mathematical structures that have been developed to work with higher dimensions, such as quaternions and octonions.

Why are there no 3 dimensional "complex numbers"?