Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Textbook Question

Chapter 2.4, Problem 1P

For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly find x , y , r , θ in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also plot the complex conjugate of the number.

1 + i

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Chapter 1.16, Problem 31MP

Chapter 2.4, Problem 2P

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For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly find æ, Y, r, 0 in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also plot the complex conjugate of the number. 1. 1+i 2. i - 1 3. 1- iv3 4. -v3+i 5. 2i 6. -4i 7. -1 8. 3 9. 2i – 2 10. 2 – 2i 11. 2 ( cos +i sin 2т 37 12. 4 i sin 13. + i sin COS Cos 2 2 14. 2 (cos + 2 ( cos 15. COS IT i sin 7 16. 5(cos 0 + i sin 0) Vze-iz/4 17. 18. 3e/2 19. 5(cos 20° + i sin 20°) 20. 7(cos 110° – i sin 110°)

įl1 + ¿13 Which of the following is equivalent to the complex number shown above? Note: i = V-1

Directions: Set your calculators on radians at this point. Do not round off during intermediate solutions. Use 3 decimal places (if applicable) in your final answer. For complex numbers, use this format (a+jb): 1. No spaces in between! 2. Use 'j' as the imaginary number 3. Use 3 decimal places (if applicable) for Real and Imaginary parts. Ex. 1.247+j0.557, 1.5-j0.5 Calculate the 3-point DFT of the given sequence: x(n) = [10 -1]

Chapter 2 Solutions

Mathematical Methods in the Physical Sciences

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