As of May 4 2007 the scripts will autodetect your timezone settings. Nothing here has to be changed, but there are a few things

## 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).

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)