33. If z1 = a + bi, find a, b, and |zil. 34. Find the polar form of z1- In Exercises 35-38, write the complex number in standard form. 35. 6(cos 30 + i sin 30) 36. 3(cos 150 + i sin 150) 4 TT 37. 2.5 cos 4 TT + i sin 3 38. 4(cos 2.5 + i sin 2.5) In Exercises 43 and 44, write the complex numbers z1 . Z2 and z1/Z2 in polar form. 43. z1 = 3(cos 30 + i sin 30) and z2 = 4(cos 60 + i sin 60) 44. z1 = 5(cos 20 + i sin 209) and z2 = -2(cos 45 + i sin 459) In Exercises 45-48, use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in (a) polar form and (b) standard form. 15 45. 3 cos - + i sin 4 18 46. [2 ( cos #2 + i sin 12In Exercises 1-6, let u = (2, -1), v = (4, 2), and w = (1, -3) be vectors. Find the indicated expression. 1. u - V 2. 2u - 3w 3. Ju+ v 4. w - 2u 5. u . V 6. u . w Use an algebraic method in Exercises 15-18 to convert the polar coordinates to rectangular coordinates. Approximate exact values with a calculator when appropriate. 15. (-2.5, 250) 16. (-3.1, 1350) Use an algebraic method in Exercises 21-24 to find the polar coordi- nates of the given rectangular coordinates of point P that satisfy the stated conditions. Approximate exact values with a calculator when appropriate. (a) OSOS 2TT 21. P = (2, -3) 22. P = (-10, 0) Exercises 33 and 34 refer to the complex number z) shown in the figure. Imaginary axis Real -3 axis