PreCalculus: Chapter 9 Test Review

Name: Class: Date:ID: APreCalculus: Chapter 9 Test ReviewShort Answer1. Plot the point given in polar coordinates.3. Plot the point given in polar coordinates.(-4, -225 )4. The polar coordinates of a point are given. Findthe rectangular coordinates of the point.2. Plot the point given in polar coordinates.5. The polar coordinates of a point are given. Findthe rectangular coordinates of the point.(-3, -135 )6. The rectangular coordinates of a point aregiven. Find polar coordinates for the point.(0, -4)7. The letters x and y represent rectangularcoordinates. Write the equation using polarcoordinates (r, θ).x2 3y1

Name:ID: A8. The letters x and y represent rectangularcoordinates. Write the equation using polarcoordinates (r, θ).13. Plot the complex number in the complex plane.2 5i2xy 19. The letters r and θ represent polar coordinates.Write the equation using rectangularcoordinates (x, y).r 1 2 sin θ10. The letters r and θ represent polar coordinates.Write the equation using rectangularcoordinates (x, y).14. Plot the complex number in the complex plane.r 10 sin θ-8 11. The letters r and θ represent polar coordinates.Write the equation using rectangularcoordinates (x, y).ir 2(sin θ - cos θ)12. Transform the polar equation to an equation inrectangular coordinates. Then identify andgraph the equation.r 2 sin θ15. Write the complex number in polar form.Express the argument in degrees, rounded to thenearest tenth, if necessary.-i16. Write the complex number in polar form.Express the argument in degrees, rounded to thenearest tenth, if necessary.-52

Name:ID: A17. Write the complex number in rectangular form.23. Find zw oras specified. Leave your answerin polar form.8z 1 iw -iFind zw.18. Write the complex number in rectangular form.4(cos 300 i sin 300 )24. Find zw or19. Find zw oras specified. Leave your answeras specified. Leave your answerin polar form.in polar form.z 1-iz 10(cos 30 i sin 30 )w 5(cos 10 i sin 10 )Find zw.20. Find zw orw 1Findas specified. Leave your answeri.25. Write the expression in the standard form a bi.in polar form.3z 5(cos 35 i sin 35 )w 2(cos 40 i sin 40 )Find zw.21. Find zw or26. Write the expression in the standard form a bi.as specified. Leave your answer4in polar form.27. Write the expression in the standard form a bi.z 6(w 12Find zw.22. Find zw or i)628. Find all the complex roots. Leave your answersin polar form with the argument in degrees.as specified. Leave your answerThe complex fourth roots of -16in polar form.29. Find all the complex roots. Leave your answersin polar form with the argument in degrees.z The complex fifth roots of -2iw Find.3

Name:ID: A30. Use the vectors in the figure below to graph thefollowing vector.31. Use the vectors in the figure below to graph thefollowing vector.u zv-w4

Name:ID: A35. The vector v has initial point P and terminalpoint Q. Write v in the form ai bj; that is, findits position vector.32. Use the vectors in the figure below to graph thefollowing vector.P (3, 3); Q (-2, -5)36. Find the indicated quantity.Find u - v given u -2i - 2j and v 7i 7j.37. Find the indicated quantity.If v 3i - 5j and w -7i 4j, find 3v - 4w.2u - z - w38. Find the indicated quantity.If v -i - j, find.39. Find the quantity if v 5i - 7j and w 3i 2j. 40. Find the quantity if v 5i - 7j and w 3i 2j.33. Use the figure below. Determine whether thegiven statement is true or false.41. Find the unit vector having the same directionas v.v -3j42. Find the unit vector having the same directionas v.A H Fv -4i - 3j34. Use the figure below. Determine whether thegiven statement is true or false.A B C D E 05

ID: APreCalculus: Chapter 9 Test ReviewAnswer SectionSHORT ANSWER1. ANS:PTS: 12. ANS:PTS: 11

ID: A3. ANS:PTS: 14. ANS:PTS: 15. ANS:PTS: 16. ANS:PTS: 17. ANS:r cos2 θ 3 sin θPTS: 18. ANS:r2 sin 2θ 1PTS: 19. ANS:x2 y2 2yPTS: 12

ID: A10. ANS:x2 y2 10yPTS: 111. ANS:x2 y2 2y - 2xPTS: 112. ANS:x2 (y - 1)2 1; circle, radius 1, center at (0, 1) in rectangular coordinatesPTS: 113. ANS:PTS: 13

ID: A14. ANS:PTS: 115. ANS:2(cos 330 i sin 330 )PTS: 116. ANS:5(cos 180 i sin 180 )PTS: 117. ANS:4 4iPTS: 118. ANS:2-2iPTS: 119. ANS:50(cos 40 i sin 40 )PTS: 120. ANS:10(cos 75 i sin 75 )PTS: 121. ANS:72PTS: 14

ID: A22. ANS:PTS: 123. ANS:2(cos 15 i sin 15 )PTS: 124. ANS:(cos 15 i sin 15 )PTS: 125. ANS:4 4iPTS: 126. ANS:-4PTS: 127. ANS:-64PTS: 128. ANS:2(cos 45 i sin 45 ), 2(cos 135 i sin 135 ), 2(cos 225 i sin 225 ), 16(cos 315 i sin 315 )PTS: 129. ANS:(cos 54 i sin 54 ),(cos 126 i sin 126 ),(cos 198 i sin 198 ),PTS: 15(cos 270 i sin 270 ),

ID: A30. ANS:PTS: 131. ANS:PTS: 132. ANS:PTS: 133. ANS:TruePTS: 16

ID: A34. ANS:TruePTS: 135. ANS:v -5i - 8jPTS: 136. ANS:-9i - 9jPTS: 137. ANS:37i - 31jPTS: 138. ANS:PTS: 139. ANS: PTS: 140. ANS:PTS: 141. ANS:u -jPTS: 142. ANS:u -i-jPTS: 17

Name: _ ID: A 3 17. Write the complex number in rectangular form. 8 18. Write the complex number in rectangular form. 4(cos 300 i sin 300 ) 19. Find zw or as specified. Leave your answer in polar form. z 10(cos 30 i sin 30 ) w 5(cos 10 i sin 10 ) Find zw. 20. Find zw or as specified. Leave your answer in polar form.