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

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* and so on
* and so on


== Chapter 4 ==
== Chapter 4 Magical Complex Numbers ==


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].  

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