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The image of the curve y = − 2 , 2 under w = z 2 and sketch it. The curve is y = − 2 , 2 . The mapping is w = z 2 . The complex number for y = − 2 , 2 is of the form z = x + i y . w = z 2 = ( x + i y ) 2 = x 2 + 2 x × i y + ( i y ) 2 = x 2 − y 2 + 2 x y i When y = − 2 , w = x 2 − ( − 2 ) 2 + 2 x ( − 2 ) i = x 2 − 4 − 4 x i That is, u = x 2 − 4 and v = − 2 x x = ± u + 4 and x = − v 2 ± u + 4 = − v 2 u + 4 = v 2 4 When y = 2 , w = x 2 − ( 2 ) 2 + 2 x ( 2 ) i = x 2 − 4 + 4 x i That is, u = x 2 − 4 and v = 2 x x = ± u + 4 and x = v 2 ± u + 4 = v 2 u + 4 = v 2 4 Use online graphing calculator and obtain the image of the curve y = − 2 , 2 as shown below in Figure 1. In Figure 1, the curve y = − 2 , 2 is mapped under w = z 2 onto w -plane.

The image of the curve y = − 2 , 2 under w = z 2 and sketch it. The curve is y = − 2 , 2 . The mapping is w = z 2 . The complex number for y = − 2 , 2 is of the form z = x + i y . w = z 2 = ( x + i y ) 2 = x 2 + 2 x × i y + ( i y ) 2 = x 2 − y 2 + 2 x y i When y = − 2 , w = x 2 − ( − 2 ) 2 + 2 x ( − 2 ) i = x 2 − 4 − 4 x i That is, u = x 2 − 4 and v = − 2 x x = ± u + 4 and x = − v 2 ± u + 4 = − v 2 u + 4 = v 2 4 When y = 2 , w = x 2 − ( 2 ) 2 + 2 x ( 2 ) i = x 2 − 4 + 4 x i That is, u = x 2 − 4 and v = 2 x x = ± u + 4 and x = v 2 ± u + 4 = v 2 u + 4 = v 2 4 Use online graphing calculator and obtain the image of the curve y = − 2 , 2 as shown below in Figure 1. In Figure 1, the curve y = − 2 , 2 is mapped under w = z 2 onto w -plane.

Advanced Engineering Mathematics

Advanced Engineering Mathematics

10th Edition

ISBN: 9780470458365

Author: Erwin Kreyszig

Publisher: Wiley, John & Sons, Incorporated

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Advanced Engineering Mathematics

Ch. 17.1 - Prob. 1P Ch. 17.1 - Prob. 2P Ch. 17.1 - Prob. 3P Ch. 17.1 - Prob. 4P Ch. 17.1 - Prob. 5P Ch. 17.1 - Prob. 6P Ch. 17.1 - Prob. 7P Ch. 17.1 - Prob. 8P Ch. 17.1 - Prob. 9P Ch. 17.1 - Prob. 11P

Ch. 17.1 - Prob. 12P Ch. 17.1 - Prob. 13P Ch. 17.1 - Prob. 14P Ch. 17.1 - Prob. 15P Ch. 17.1 - Prob. 16P Ch. 17.1 - Prob. 17P Ch. 17.1 - Prob. 18P Ch. 17.1 - Prob. 19P Ch. 17.1 - Prob. 20P Ch. 17.1 - Prob. 21P Ch. 17.1 - Prob. 22P Ch. 17.1 - Prob. 23P Ch. 17.1 - Prob. 24P Ch. 17.1 - Prob. 25P Ch. 17.1 - Prob. 26P Ch. 17.1 - Prob. 27P Ch. 17.1 - Prob. 29P Ch. 17.1 - Prob. 30P Ch. 17.1 - Prob. 31P Ch. 17.1 - Prob. 32P Ch. 17.1 - Prob. 33P Ch. 17.1 - Prob. 34P Ch. 17.1 - Prob. 35P Ch. 17.2 - Prob. 1P Ch. 17.2 - Prob. 2P Ch. 17.2 - Prob. 3P Ch. 17.2 - Prob. 4P Ch. 17.2 - Prob. 5P Ch. 17.2 - Prob. 6P Ch. 17.2 - Prob. 7P Ch. 17.2 - Prob. 8P Ch. 17.2 - Prob. 9P Ch. 17.2 - Prob. 10P Ch. 17.2 - Prob. 11P Ch. 17.2 - Prob. 12P Ch. 17.2 - Prob. 13P Ch. 17.2 - Prob. 14P Ch. 17.2 - Prob. 15P Ch. 17.2 - Prob. 16P Ch. 17.2 - Prob. 17P Ch. 17.2 - Prob. 18P Ch. 17.2 - Prob. 19P Ch. 17.2 - Prob. 20P Ch. 17.3 - Prob. 8P Ch. 17.3 - Prob. 9P Ch. 17.3 - Prob. 10P Ch. 17.3 - Prob. 11P Ch. 17.3 - Prob. 12P Ch. 17.3 - Prob. 13P Ch. 17.3 - Prob. 14P Ch. 17.3 - Prob. 15P Ch. 17.3 - Prob. 16P Ch. 17.3 - Prob. 17P Ch. 17.4 - Prob. 1P Ch. 17.4 - Prob. 2P Ch. 17.4 - Prob. 3P Ch. 17.4 - Prob. 4P Ch. 17.4 - Prob. 5P Ch. 17.4 - Prob. 6P Ch. 17.4 - Prob. 7P Ch. 17.4 - Prob. 9P Ch. 17.4 - Prob. 10P Ch. 17.4 - Prob. 11P Ch. 17.4 - Prob. 15P Ch. 17.4 - Prob. 16P Ch. 17.4 - Prob. 17P Ch. 17.4 - Prob. 18P Ch. 17.4 - Prob. 19P Ch. 17.4 - Prob. 20P Ch. 17.4 - Prob. 21P Ch. 17.4 - Prob. 22P Ch. 17.4 - Prob. 25P Ch. 17.5 - Prob. 1P Ch. 17.5 - Prob. 2P Ch. 17.5 - Prob. 5P Ch. 17.5 - Prob. 7P Ch. 17.5 - Prob. 10P Ch. 17 - Prob. 1RQ Ch. 17 - Prob. 2RQ Ch. 17 - Prob. 3RQ Ch. 17 - Prob. 4RQ Ch. 17 - Prob. 5RQ Ch. 17 - Prob. 6RQ Ch. 17 - Prob. 7RQ Ch. 17 - Prob. 8RQ Ch. 17 - Prob. 9RQ Ch. 17 - Prob. 10RQ Ch. 17 - Prob. 11RQ Ch. 17 - Prob. 12RQ Ch. 17 - Prob. 13RQ Ch. 17 - Prob. 14RQ Ch. 17 - Prob. 15RQ Ch. 17 - Prob. 16RQ Ch. 17 - Prob. 17RQ Ch. 17 - Prob. 18RQ Ch. 17 - Prob. 19RQ Ch. 17 - Prob. 20RQ Ch. 17 - Prob. 21RQ Ch. 17 - Prob. 23RQ Ch. 17 - Prob. 24RQ Ch. 17 - Prob. 25RQ Ch. 17 - Prob. 26RQ Ch. 17 - Prob. 27RQ Ch. 17 - Prob. 28RQ Ch. 17 - Prob. 39RQ

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