Chap 1 The Number System

We sometimes say that addition of complex numbers

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

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