Mathematic Methods HW Solutions 6

# Mathematic Methods HW Solutions 6 - 5.64 Straight lines y =...

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Chapter 2 6 5.19 (2 + 3 i ) / 13; ( x - yi ) / ( x 2 + y 2 ) 5.20 ( - 5 + 12 i ) / 169; ( x 2 - y 2 - 2 ixy ) / ( x 2 + y 2 ) 2 5.21 (1 + i ) / 6; ( x + 1 - iy ) / [( x + 1) 2 + y 2 ] 5.22 (1 + 2 i ) / 10; [ x - i ( y - 1)] / [ x 2 + ( y - 1) 2 ] 5.23 ( - 6 - 3 i ) / 5; (1 - x 2 - y 2 + 2 yi ) / [(1 - x ) 2 + y 2 ] 5.24 ( - 5 - 12 i ) / 13; ( x 2 - y 2 + 2 ixy ) / ( x 2 + y 2 ) 5.26 1 5.27 r 13 / 2 5.28 1 5.29 5 5 5.30 3 / 2 5.31 1 5.32 169 5.33 5 5.34 1 5.35 x = - 4, y = 3 5.36 x = - 1 / 2, y = 3 5.37 x = y = 0 5.38 x = - 7, y = 2 5.39 x = y = any real number 5.40 x = 0, y = 3 5.41 x = 1, y = - 1 5.42 x = - 1 / 7, y = - 10 / 7 5.43 ( x,y ) = (0 , 0), or (1 , 1), or ( - 1 , 1) 5.44 x = 0, y = - 2 5.45 x = 0, any real y ; or y = 0, any real x 5.46 y = - x 5.47 ( x,y ) = ( - 1 , 0), (1 / 2 , ± 3 / 2) 5.48 x = 36 / 13, y = 2 / 13 5.49 x = 1 / 2, y = 0 5.50 x = 0, y 0 5.51 Circle, center at origin, radius = 2 5.52 y axis 5.53 Circle, center at (1 , 0), r = 1 5.54 Disk, center at (1 , 0), r = 1 5.55 Line y = 5 / 2 5.56 Positive y axis 5.57 Hyperbola, x 2 - y 2 = 4 5.58 Half plane, x > 2 5.59 Circle, center at (0 , - 3), r = 4 5.60 Circle, center at (1 , - 1), r = 2 5.61 Half plane, y < 0 5.62 Ellipse, foci at (1 , 0) and ( - 1 , 0), semi-major axis = 4 5.63 The coordinate axes
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Unformatted text preview: 5.64 Straight lines, y = ± x 5.67 v = (4 t 2 + 1)-1 , a = 4(4 t 2 + 1)-3 / 2 5.68 Motion around circle r = 1, with v = 2, a = 4 6.2 D , ρ = √ 2 6.3 C , ρ = 1 / √ 2 6.4 D , | a n | = 1 n→ 6.5 D 6.6 C 6.7 D , ρ = √ 2 6.8 D , | a n | = 1 n→ 6.9 C 6.10 C , ρ = √ 2 / 2 6.11 C , ρ = 1 / 5 6.12 C 6.13 C , ρ = r 2 / 5 7.1 All z 7.2 | z | < 1 7.3 All z 7.4 | z | < 1 7.5 | z | < 2 7.6 | z | < 1 / 3 7.7 All z 7.8 All z 7.9 | z | < 1 7.10 | z | < 1 7.11 | z | < 27 7.12 | z | < 4 7.13 | z-i | < 1 7.14 | z-2 i | < 1 7.15 | z-(2-i ) | < 2 7.16 | z + ( i-3) | < 1 / √ 2 8.3 See Problem 17.30....
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