Exercise 4.4.15. Consider a plane with Cartesian coordinates. Let O be the point (0, 0), let A be the point (a, b), and let C be the point (c,d). Also, let w = a + bi and z = c+di. We may consider the three complex numbers 0, w, z as representing the vertices of triangle OAC. (A word to the wise: drawing a picture can be extremely helpful.) (a) Express the lengths of the three sides of the triangle in terms of w and z. For example, the length of side OA is |w|. (b) Show that multiplying 0, w, and z by rotates the triangle so that side OA lies along the real axis (you may use polar coordinates). (c) Let 0, w', and z' be the three vertices of the rotated triangle. Show that Re[2¹] = and Im[2] = 2w| 2 w
Exercise 4.4.15. Consider a plane with Cartesian coordinates. Let O be the point (0, 0), let A be the point (a, b), and let C be the point (c,d). Also, let w = a + bi and z = c+di. We may consider the three complex numbers 0, w, z as representing the vertices of triangle OAC. (A word to the wise: drawing a picture can be extremely helpful.) (a) Express the lengths of the three sides of the triangle in terms of w and z. For example, the length of side OA is |w|. (b) Show that multiplying 0, w, and z by rotates the triangle so that side OA lies along the real axis (you may use polar coordinates). (c) Let 0, w', and z' be the three vertices of the rotated triangle. Show that Re[2¹] = and Im[2] = 2w| 2 w
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.5: Reflections And Symmetry
Problem 20E
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Please do part ABC and please show step by step and explain
![Exercise 4.4.15. Consider a plane with Cartesian coordinates. Let O be
the point (0, 0), let A be the point (a, b), and let C be the point (c,d). Also,
let w = a + bi and z = c+di. We may consider the three complex numbers
0, w, z as representing the vertices of triangle OAC.
(A word to the wise: drawing a picture can be extremely helpful.)
(a) Express the lengths of the three sides of the triangle in terms of w and
z. For example, the length of side OA is |w|.
(b) Show that multiplying 0, w, and z by rotates the triangle so that
side OA lies along the real axis (you may use polar coordinates).
(c) Let 0, w', and z' be the three vertices of the rotated triangle. Show that
Re[2¹] = and Im[2] =
2w|
2 w](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F892e817a-9b32-4eeb-b8fc-5dd7ffde6479%2Faddd8355-320d-4d85-9ccf-608dca7fc909%2F74nrks_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 4.4.15. Consider a plane with Cartesian coordinates. Let O be
the point (0, 0), let A be the point (a, b), and let C be the point (c,d). Also,
let w = a + bi and z = c+di. We may consider the three complex numbers
0, w, z as representing the vertices of triangle OAC.
(A word to the wise: drawing a picture can be extremely helpful.)
(a) Express the lengths of the three sides of the triangle in terms of w and
z. For example, the length of side OA is |w|.
(b) Show that multiplying 0, w, and z by rotates the triangle so that
side OA lies along the real axis (you may use polar coordinates).
(c) Let 0, w', and z' be the three vertices of the rotated triangle. Show that
Re[2¹] = and Im[2] =
2w|
2 w
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