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Mathematics
9thgrade
Review Complex Numbers and the Polar Coordinate Plane
32 questions
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- 1. Multiple ChoiceFind the absolute value of the complex number. Also state what quadrant the point would land in.
2 + 3i√13, Quadrant 1√5, Quadrant 1√11, Quadrant 2√11, Quadrant 3 - 2. Multiple ChoiceFind the absolute value of the complex number. Also state what quadrant the point would land in.
-3 + i√10, Quadrant 2√10, Quadrant 32, Quadrant 23, Quadrant 3 - 3. Multiple ChoiceExpress the complex number in polar form.
-2 + 5i5.39 ( cos 1.95 + i sin 1.95)5.39 ( cos 65.06 + i sin 65.06)2.65 ( cos 1.95 - i sin 1.95 )2.65 ( cos 65. 06 - i sin 65.06 ) - 4. Multiple ChoiceWhat class are you in?PrecalculusAlgebra 2Algebra 1P.E
- 5. Multiple ChoiceExpress the complex number in polar form.
6 + 2i6.32 ( cos 0.32 + i sin 0.32)6.32 ( cos 0.45 + i sin 0.45)1.73 ( cos 0.32 + i sin 0.32)1.73 ( cos 0.45 - i sin 0.45) - 6. Multiple ChoiceWhat quadrant would the point in polar form land in?
4 ( cos π /3 + i sin π /3)Quadrant 4Quadrant 1Quadrant 2Quadrant 3 - 7. Multiple ChoiceExpress the point in polar form in rectangular form.
4 ( cos π /3 + i sin π /3)2 + 2√3 i2 + √3 i2 - 2√3 i-2 + 2√3 i - 8. Multiple ChoiceFind
5(cos 2π /3 + i sin 2π /3)⋅2( cos π /3 + i sin π /3)
in polar form. Then express your final answer in rectangular form.-1010-10i10i - 9. Multiple ChoiceFind
1/2 ( cos π /3 + i sin π /3)
÷ 3 ( cos π /6 + i sin π /6)
and express your final answer in rectangular form.√3/12 + 1/12 i12√3 + 12 i√3/12 - 1/12 i12√3 - 12i - 10. Multiple ChoiceFind
(3 + 3√3 i )4
using De Moivre's Theorem and express your answer in rectangular form.-648 - 648 √3 i-654 - 654 √3 i-1962 - 1962 √3 i648 i - 11. Multiple ChoiceConvert the rectangular coordinates to polar form(√2 , 7π/4)(2 , 3π/4)(4 , π/4)(4 , 5π/4)
- 12. Multiple ChoiceConvert the polar coordinates to rectangular form( -3, 3)(3, 3√3)(-3, 3√3)(3, -3√3)
- 13. Multiple ChoiceCovert the rectangular equation to polar formr² = 81r = 3r = 4.5r sin θ = 9
- 14. Multiple ChoiceCovert the rectangular equation to polar formr = cot θ csc θr = tan θ csc θr = tan θ sec θr = 0
- 15. Multiple ChoiceCovert the rectangular equation to polar formr sin θ = 4r = 4 csc θr = sec θ ∕ 4r = 4 sec θ
- 16. Multiple ChoiceConvert the polar equation to rectangular formx² + y² = 49x = 7x + y = 49x² + y² = 7
- 17. Multiple ChoiceConvert the polar equation to rectangular formx = 2 cos θx = 2y = 2x² + y² = 2
- 18. Multiple ChoiceConvert the polar equation to rectangular formy = xx = 0y = 0tan θ = 0
- 19. Multiple ChoiceWhich point represents (3, 3π/4)FEBA
- 20. Multiple ChoiceWhich point represents the polar coordinate
(-4, -2π/3)BFDA - 21. Multiple ChoiceWhich point represents the polar coordinate
(-2, -5π/6)BFDC - 22. Multiple ChoiceWhich equation represents the polar graph?r = sin θr = sin 4θr = 4 sin θr = 4 cos θ
- 23. Multiple ChoiceWhich equation represents the polar graph?r = 6 + 6 sin θr = 12 sin θr = 4 - 3 sin θr = 4 + 5 sin θ
- 24. Multiple ChoiceWhich equation represents the polar graph?r = sin 4θr = 6 sin 2θr = 6 cos 2θr = cos 4θ
- 25. Multiple ChoiceConvert -1 + i to Polar (cis) Form.√2 cis(3π/4)√2 cis(π/4)cis(-π/4)cis(3π/4)
- 26. Multiple ChoiceConvert 5√3 - 5i to Polar (cis) Form.√40 cis(11π/6)10 cis(π/6)10 cis(11π/6)√40 cis(-π/6)
- 27. Multiple ChoiceDescribe the curveRose with 3 leavesRose with 6 leavesInner loop limaconCircle
- 28. Multiple ChoiceDescribe the curveCardioidCircleInner loop limaconRose with 6 leaves
- 29. Multiple ChoiceDescribe the curveRose with 3 leavesCircleCardioidInner loop limacon
- 30. Multiple ChoiceIn Polar coordinates what is x equal to?rsinΘrcosΘx²+y²tan⁻¹(y/x)
- 31. Multiple ChoiceConvert into rectangular form
r = 2cos(@)x + y = 2xx2 + y2 = 2xx2+y2 = 2cos2(@)r = 2x - 32. Multiple ChoiceUse DeMoivre's Theorem, write your answer in complex form.
(1 - i)78 + 8i4 + 4i32 + 32i16 + 16i - Answer choicesTagsAnswer choicesTags