{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}


MAT1341-L01-ComplexNumbers - COMPLEX NUMBERS JOSE...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
COMPLEX NUMBERS JOS ´ E MALAG ´ ON-L ´ OPEZ What is a Number? Numbers are “symbols” used for measuring and counting purposes. Examples of numbers are: Natural Numbers: N = { 0 , 1 , 2 , 3 , . . . } ; Integers: Z = { 0 , ± 1 , ± 2 , ± 3 , . . . } ; Rationals: Q = { a b | a and b are integers } . All these numbers are part of a larger collection of such symbols, the Real Numbers , denoted by R . Are There More Numbers? From Calculus we know that there is another collection of numbers, the irrationals. We can say, in short, that the irrationals are the real numbers that are not rationals. For a more precise definition we need to consider limits, which we will avoid since is not part of this course. Examples of irrational numbers are: 2, π , e , etc. In general, numbers have been “obtained” when we want to consider the solution set of a given type of equations. For example, the integers are obtained from equations of the form x + a = 0 , a N , or the rationals, obtained from equations of the form ax = b, a, b Z . In this course we will consider two extensions of the real numbers, the complex numbers and matrices. Complex Numbers The complex numbers are the solutions of equations of the form x 2 = a, a R . 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Fortunately, we only need to be concerned with the solution of x 2 = 1. Definition. The symbol ı = 1 will be called the imaginary unit . Notice that ı 2 = 1. Definition. The complex numbers , denoted by C , are defined as the collection of ALL the expressions of the form a + b ı, a, b R .
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 5

MAT1341-L01-ComplexNumbers - COMPLEX NUMBERS JOSE...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online