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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. ½(e^(iz) + e^(-iz))






2. 2a






3. 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






4. y / r






5. 1






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






7. 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






8. I






9. ? = -tan?






10. R?¹(cos? - isin?)






11. 1






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






13. To prove that number field every algebraic equation in z with complex coefficients has a solution we need

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14. When two complex numbers are multipiled together.






15. A number that can be expressed as a fraction p/q where q is not equal to 0.






16. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n






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






18. Multiply moduli and add arguments






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






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






21. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....






22. In this amazing number field every algebraic equation in z with complex coefficients






23. 5th. Rule of Complex Arithmetic






24. I = imaginary unit - i² = -1 or i = v-1






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

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






27. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






28. To simplify a complex fraction






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






30. Imaginary number

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






32. The reals are just the






33. To simplify the square root of a negative number






34. For real a and b - a + bi =






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






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






37. Any number not rational






38. ½(e^(-y) +e^(y)) = cosh y






39. 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






40. I






41. Root negative - has letter i






42. 2nd. Rule of Complex Arithmetic

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43. We consider the a real number x to be the complex number x+ 0i and in this way we can think of the real numbers as a subset of






44. The complex number z representing a+bi.






45. A complex number may be taken to the power of another complex number.






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






47. When two complex numbers are added together.






48. Real and imaginary numbers






49. Derives z = a+bi






50. A number that cannot be expressed as a fraction for any integer.







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