In Exercises 1-18, s = 1 + 2i, u = 3 – 2i, v = 4 + i, w = 2 - i, and z = 1+i. In each exercise, perform the indicated calculation and express the result in the form a + ib. 1. u 4. Z + w 7. vv 10. z²w 13. u/v 16. (w+v)/u 2. Z 5. u + ū 8. uv 11. uw² 14. v/u² 17. w + iz 3. u + v 6. s-5 9. s² - w 12. s(u² + v) 15. s/z 18. s - iw Find the eigenvalues and the eigenvectors for the matri- ces in Exercises 19-24. (For the matrix in Exercise 24, one eigenvalue is λ = 1 + 5i.) 21. -2-1 52 23.1 -4 -1 2 3 13 3 In Exercises 25 and 26, solv 25. (1 + i)x +iy = 5+ (1 - i)x - 4y = -11 +
In Exercises 1-18, s = 1 + 2i, u = 3 – 2i, v = 4 + i, w = 2 - i, and z = 1+i. In each exercise, perform the indicated calculation and express the result in the form a + ib. 1. u 4. Z + w 7. vv 10. z²w 13. u/v 16. (w+v)/u 2. Z 5. u + ū 8. uv 11. uw² 14. v/u² 17. w + iz 3. u + v 6. s-5 9. s² - w 12. s(u² + v) 15. s/z 18. s - iw Find the eigenvalues and the eigenvectors for the matri- ces in Exercises 19-24. (For the matrix in Exercise 24, one eigenvalue is λ = 1 + 5i.) 21. -2-1 52 23.1 -4 -1 2 3 13 3 In Exercises 25 and 26, solv 25. (1 + i)x +iy = 5+ (1 - i)x - 4y = -11 +
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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