Difference between revisions of "The Road to Reality Study Notes"

* and so on

* and so on

Penrose introduced the complex numbers, extending addition, subtraction, multiplication, and division of the reals to the system obtained by adjoining i, the square root of -1. Polynomial equations can be solved by complex numbers, this property is called ''[https://en.wikipedia.org/wiki/Algebraically_closed_field algebraic closure]'' and follows from the [https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra Fundamental Theorem of Algebra].  

Penrose introduced the complex numbers, extending addition, subtraction, multiplication, and division of the reals to the system obtained by adjoining i, the square root of -1. Polynomial equations can be solved by complex numbers, this property is called ''[https://en.wikipedia.org/wiki/Algebraically_closed_field algebraic closure]'' and follows from the [https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra Fundamental Theorem of Algebra].