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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • 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. To simplify the square root of a negative number






2. 1






3. 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






4. ½(e^(-y) +e^(y)) = cosh y






5. 1






6. Any number not rational






7. Have radical






8. The field of all rational and irrational numbers.






9. x + iy = r(cos? + isin?) = re^(i?)






10. All the powers of i can be written as






11. 1st. Rule of Complex Arithmetic






12. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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

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






15. The reals are just the






16. A² + b² - real and non negative






17. 3rd. Rule of Complex Arithmetic






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






19. The modulus of the complex number z= a + ib now can be interpreted as






20. When two complex numbers are multipiled together.






21. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1






22. Imaginary number

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23. 1. i^2 = -1 2. Every complex number has the 'Standard Form': a + bi for some real a and b. 3. For real a and b - a + bi = 0 if and only if a = b = 0 4. (a + bi) = (c + bi) = (a + c) + ( b + d)i 5. (a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc






24. Where the curvature of the graph changes






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






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






27. V(x² + y²) = |z|






28. A + bi






29. Equivalent to an Imaginary Unit.






30. The field of numbers of the form - where and are real numbers and i is the imaginary unit equal to the square root of - . When a single letter is used to denote a complex number - it is sometimes called an 'affix.'






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






32. Real and imaginary numbers






33. ½(e^(iz) + e^(-iz))






34. E^(ln r) e^(i?) e^(2pin)






35. 2a






36. 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






37. Numbers on a numberline






38. 1






39. No i






40. (2+i)(2i-3) you would use the foil methom which is first outter inner last. (2x2i)(2x-3)(ix2i^2)(ix(-3) =i-8






41. xpressions such as ``the complex number z'' - and ``the point z'' are now






42. Like pi






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






44. The square root of -1.






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






46. We can also think of the point z= a+ ib as






47. A complex number and its conjugate






48. A subset within a field.






49. All numbers






50. 3






Can you answer 50 questions in 15 minutes?



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