m25-hw3 - i = -1. Complex numbers are added according to...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 25: Advanced Calculus Fall 2010 Homework # 3 Due Date: Friday, October 15 Reading: Finish reading sections 1.1-1.3. Read sections 1.4-1.6. Complete the following problems from the textbook: 1.3.7, 1.4.1, 1.4.3, 1.6.1, 1.6.2, 1.6.10, 1.6.17 In addition, please complete the following problems: 3.1: Use the field axioms in § 1.3 and the ordered field axioms in § 1.4 to prove the following statements for an ordered field F . As before, you must justify each of your steps. (I). Show that x 2 0 for any x F . (II). Show that 1 > 0. (II). Show that if x F and x > 1, then 0 < x - 1 < 1. 3.2: The complex numbers are the field C = { a + bi : a,b R } , where
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: i = -1. Complex numbers are added according to the rule ( a + bi ) + ( c + di ) = ( a + c ) + ( b + d ) i, and complex numbers are multiplied according to the rule ( a + bi ) ( c + di ) = ( a-d ) + ( b + c ) i. (Notice that the multiplication is just obtained by FOILing.) Dene an order on the complex numbers by declaring that a + bi c + di, if a c AND b d . Does this turn C into an ordered eld? Why or why not? Be sure to justify your answers! (You only need to check axioms O1-O4. Dont worry about showing that C is a eld.) 1...
View Full Document

This note was uploaded on 03/18/2012 for the course MAT MAT 25 taught by Professor Stevenklee during the Fall '10 term at UC Davis.

Ask a homework question - tutors are online