828 CHAPTER 8 Applications of Trigonometry 8.5 Exercises CONCEPT PREVIEW For each complex number shown, give (a) its rectangular form and (b) its trigonometric (polar) form with r 70, 0° … u 6360°. Imaginary –2 –1 1 2 –2 –1 1 2 Real 0 2. Imaginary –2 –1 1 2 –2 –1 1 2 Real 0 3. Imaginary –2 –1 1 2 –2 –1 1 2 Real 0 1. Imaginary –2 –1 1 2 –2 –1 1 2 Real 0 5. Imaginary –2 –1 1 2 –2 –1 1 2 Real 0 6. Imaginary –2 –1 1 2 –2 1 2 Real 0 –√3 4. CONCEPT PREVIEW Fill in the blanks to correctly complete each problem. 7. When multiplying two complex numbers in trigonometric form, we their absolute values and their arguments. 8. When dividing two complex numbers in trigonometric form, we their absolute values and their arguments. 9. 351cos 150° + i sin 150°24321cos 30° + i sin 30°24 = _____ 1cos _____ + i sin _____2 = _____ + _____ i 10. 61cos 120° + i sin 120°2 21cos 30° + i sin 30°2 = _____ 1cos _____ + i sin _____2 = _____ + _____ i 11. cis1-1000°2 # cis 1000° = cis _____ = _____ + _____ i 12. 5 cis 50,000° cis 50,000° = 5 cis _____ = _____ + _____ i Graph each complex number. See Example 1. 13. -3 + 2i 14. 6 - 5i 15. 22 + 22i 16. 2 - 2i23 17. -4i 18. 3i 19. -8 20. 2 Find the sum of each pair of complex numbers. In Exercises 21 – 24, graph both complex numbers and their resultant. See Example 1. 21. 4 - 3i, -1 + 2i 22. 2 + 3i, -4 - i 23. 5 - 6i, -5 + 3i 24. 7 - 3i, -4 + 3i 25. -3, 3i 26. 6, -2i 27. -5 - 8i, -1 28. 4 - 2i, 5 29. 7 + 6i, 3i
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