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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
