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 ) |
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).
ReplyDelete