Chap 1 The Number System

# We sometimes say that addition of complex numbers

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: quired. 1.6. Polar Coordinates Since every complex number is of the form z = x + y i, where x, y ∈ R, we can identify z with the point (x, y ) on the xy -plane R2 as shown in the Argand diagram below: y +v v y ; ; n nn nn ; nnn ;nn ; nn ×o ; ; ; ; ;;; ; ;; ; ;; ;;;;;; ; ; ;; ;;; ; ; ; ; ; ; ;; ; ×o ; ; ; ;; ; ;; ; ; ; ; ; ; ×o n ; ;;;;; ;;;;;; z+w w = u + vi z = x + yi u x x+u Chapter 1 : The Number System page 8 of 19 First Year Calculus c W W L Chen, 1982, 2005 Note that the numbers z = x + y i and w = u + v i, where x, y, u, x ∈ R, are represented by the points (x, y ) and (u, v ) respectively, and that their sum z + w is represented by the point (x + u, y + v ), the vertex opposite the vertex (0, 0) in a parallelogram with (x, y ) and (u, v ) also as vertices. We sometimes say that addition of complex numbers satisﬁes the parallelogram law. To describe a product in an Argand diagram is not as straightforward. Suppose that z = x + y i, where x, y ∈ R. Consider the following Arg...
View Full Document

## This note was uploaded on 02/01/2009 for the course MATH 2343124 taught by Professor Staff during the Fall '08 term at UCSD.

Ask a homework question - tutors are online