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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. The modulus of the complex number z= a + ib now can be interpreted as






2. 2ib






3. (2i+3)/(9-i)for the denominator you multiply by the conjugate and what u do to the bottom u have to do to the top then you distribute the bottom then the top then add like terms then you simplify. 21i+25/17






4. Every complex number has the 'Standard Form':






5. zn = (cos? + isin?)n = cosn? + isinn? - For all integers n

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6. Has exactly n roots by the fundamental theorem of algebra






7. R?¹(cos? - isin?)






8. 1






9. R^2 = x






10. The reals are just the






11. A complex number and its conjugate






12. 5th. Rule of Complex Arithmetic






13. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called






14. Imaginary number

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15. z1z2* / |z2|²






16. Derives z = a+bi






17. 1






18. I^26/4= i^24 x i^2 =-1 so u divide the number by 4 and whatevers left over is the number that its equal to.






19. E^(i?) = cos? + isin? ; e^(ip) + 1 = 0

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20. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.






21. Numbers on a numberline






22. I






23. The square root of -1.






24. Multiply moduli and add arguments






25. In the same way that we think of real numbers as being points on a line - it is natural to identify a complex number z=a+ib with the point (a -b) in the cartesian plane.






26. Notice that rules 4 and 5 state that we complex numbers together - we can divide by c + di if c and d are not both zero. But there is a much easier way to do division.

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27. (e^(-y) - e^(y)) / 2i = i sinh y






28. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i






29. Equivalent to an Imaginary Unit.






30. 3rd. Rule of Complex Arithmetic






31. When you subtract two complex numbers a + bi and c + di - you get the difference of the real parts and the difference of the imaginary parts: (a + bi) - (c + di) = (a - c) + (b - d)i






32. 3






33. y / r






34. Starts at 1 - does not include 0






35. 2nd. Rule of Complex Arithmetic

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36. The field of all rational and irrational numbers.






37. Real and imaginary numbers






38. 2a






39. Formula: z1 · z2 = (a + bi)(c + di) = ac +adi +cbi +bdi² = (ac - bd) + (ad +cb)i - when you multiply a complex number by its conjugate - you get a real number.






40. 4th. Rule of Complex Arithmetic






41. When you add two complex numbers a + bi and c + di - you get the sum of the real parts and the sum of the imaginary parts: (a + bi) + (c + di) = (a + c) + (b + d)i






42. When two complex numbers are multipiled together.






43. Root negative - has letter i






44. ? = -tan?






45. We see in this way that the distance between two points z and w in the complex plane is






46. (a + bi)(c + bi) =






47. A² + b² - real and non negative






48. The product of an imaginary number and its conjugate is






49. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi






50. Not on the numberline