Homework 2

Due: April 16, 2015 at end of workday

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8. Chapter 2, Section 11, Problem 17>br> 9. Chapter 2, Section 16, Problem 1

Show that if the line through the origin and the point z is rotated by 90^o about the origin, it becomes the line through the origin and the point iz. This fact is sometimes expressed by saying that multiplying a complex number by i rotates it through 90^o. Use this idea in the following problem. Let z = ae^iwt be the diplacement of a particle from the origin at time t. Show that the particle travels in a circle of radius a at velocity v = wa and with acceleration of magnitude v²/a directed toward the center of the circle.

10. Chapter 2, Section 16, Problem 11

Prove that

cos A + cos 3A + cos 5A + ... + cos (2n-1)A = sin 2nA/(2 sin A)
sin A + sin 3A + sin 5A + ... + sin (2n-1)A = sin²nA/(sin A)


Hint: Use Euler's formula and the geometric progression formula.

11. Chapter 14, Section 3, Problem 14

12. Chapter 14, Section 3, Problem 20
13. Chapter 14, Section 9, Problem 11

14. Chapter 14, Section 9, Problem 12

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