Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Chapter 2.4, Problem 5P

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.

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Chapter 2.4, Problem 4P

Chapter 2.4, Problem 6P

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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

Find the distance between these two complex numbers: -8 + i and -3 + 8i. a. 5.2 b. 9.2 c. 6.8 d. 8.6 e. 4.8 f. 7.6

Chapter 2 Solutions

Mathematical Methods in the Physical Sciences

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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 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. 2i

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