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Sunday, December 18, 2011

Fearless Symmetry 5/23: Complex Numbers

I read the fifth chapter of Fearless Symmetry.

Part 1: Algebraic Preliminaries

Chapter 5: Complex Numbers

Well, I think it is safe to assume that readers of this blog know the complex numbers. This chapter is in fact about a subset of the Complex Numbers called the Algebraic Numbers. In FS they use $\mathbf{Q}^{Alg}$ as notation, whereas I have seen mostly the notation $A$ for the Algebraic Numbers.

Every algebraic number can be expressed as the root of of a polynomial equation with integer coefficients. So $\pi$ is not a member of $\mathbf{Q}^{Alg}$, but $\sqrt{2}$ is because $\sqrt{2}$ is a solution of $x^2 - 2 = 0$.

Visualisation of the (countable) field of algebraic numbers in the complex plane.
( From Wikipedia )
To be continued with 6. Equations and varieties

1 comment:

  1. I am here to discuss about complex numbers as A number which can be put in the form a + bi termed as complex number, where a and b are real numbers and i is called the imaginary unit,in given expression "a" is the real part and b is the imaginary part of the complex number. The complex number can be identified with the point (a, b).


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