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In Problems 11-22, plot each complex number in the complex plane and write it in polar form. Express the argument in degrees. Nadi 15, =34 m3 - 4 12-143 13. V3-i 16. -2 1.4 =4 20.2 + V3i i= tetsing In Problems 23-32, write each complex number in rectangular form. \ 23. 2(cos 120° + sin 120°) 18 18 24. 3(cos 210° + isin 210°) 3m. Sr 30. 0.4(cos 200° + isin 200°) 7 + isin— a a( cos i) 10 In Problems 3340, find zw and < Leave your answers in polar form. N33. z = 2(eos 40" + isin 40°) w = 4(cos 20° + isin 20°) 36. z = 2(cos 80° + isin 80°) w = 6(cos 200° + /sin 200°) Mitoetecrtnintins w=W3-i 34. 2 = cos 120° + isin 120° w = cos 100° + / sin 100° an z= 2( cos + isinZ) w = 2{ os = + isin 10 10. 4. 2=1-i wel V3 In Problems 41-32, write each expression in the standard form a + bi. we [von ue] 3a _ 50. (V3 — i) 42. [3(cos 80° + i sin 80°) 48. [V3 (cos 10° + isin 10°) as [V5 (so3 + isn32)P comin 14.1 - V3i 18. 9V3 4 9 2 V5-i 28, (cos 2 + isin2Z) 28. 4{ cos + isin) 35, z = 3(cos 130° + fsin 130°) w = 4(cos 270° + fsin 270°) 3a 3a = 22 + isin — 38. 2 4{ cos isin) or 9a w= 2{ cos % isin) 10 46. [Fteos 72° + isin call 491i 52, (1 — Vi)" In Problems 53-60, find all the complex roots. Leave your answers in polar form with the argument in degrees. \ 53. The complex cube roots of 1 + i "55. The complex fourth roots of 4 — 4V/3i_ _ 81, The complex fourth roots of = 167 59, The complex fifth roots of i 34. The complex fourth roots of V3-i 56. The complex cube roots of —8 — 81 58. The complex cube roots of -8 60. The complex fifth roots of -i 10.3 Assess Your Understanding (page 748) 5, real:imaginary 6, magnitude; modulus; argument 7. ryraQ) + Oy.@) +o) Be rth 9% three 10, True i. WVilcos 45° + i sin 45°) 17. 23. RS 37. 4. 53. 55. 57. 59, 13. Imaginary 15, Imaginary axi axis =3 a ands Imaginary 19. Imaginary 21. Imaginary axis axis -3 Real = 2 axis -4) 4\V3(cos 315° + isin 315°) 5(cos 306.9° + isin 306.9°) V13(cos 123.7° + isin 123.7°) -14+ V3i 25, 2V2 - 2V2i 27. -3i 29. -0.035 + 0.1971 31. 1.970 + 0.3471 z ot . . 3 . zw = 8(cos 60° + sin 60°); = 5(cos 20° + isin 20°) 38. zw = 12(cos 40° + i sin 40° 7 (cos 220° + isin 220°) = 08 5 + isin a 39. cw = 4V2(cos 15° + isin 15°); = = V/2(cos 75° + isin 75°) w= {cos + tin = . 80 w = 2 2 V2 32 + 32V3i 43.327 48, 2 + i . ae + svi, 49. 444) SL. -23 + 14.1421 ¥3(cos 15° + i sin 15°), 2 (cos 135° + isin 135°), (/2(cos 255° + i sin 255°) W&(cos 75° + isin 75°), W8(cos 165° + isin 165°), W/S(cos 255" + isin 255°), W/8(cos 345° + isin 345°) 247.5°), 2(cos 337.5° + isin 337.5") 2(cos 67.5° + i sin 67.5"), 2(cos 157.5° + isin 157.5°), 2(cos 247.5° + cos 18° + isin 18°, cos 90° + isin 90°, cos 162° + isin 162°, cos 234° + / sin 234°, cos 306° + i sin 306° 
