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The Road to Reality Study Notes: Difference between revisions
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== 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]. | ||