Gauss Representation

This lecture covers the representation of complex numbers in the Gauss plane, highlighting the addition and multiplication operations, the dimension of the real vector space of complex numbers, and the concept of bases. It explains how to implement complex number multiplication in the Gauss representation, emphasizing the perpendicularity of vectors in R². The lecture also demonstrates how rotations in R² correspond to multiplication by the imaginary unit i. Through examples, it illustrates the addition and multiplication of complex numbers in the Gauss representation. The lecture concludes by showing how R² can be viewed as a complex vector space, with complex numbers acting on elements of R² through matrix multiplication.