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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. 4th. Rule of Complex Arithmetic






2. (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






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






4. 2nd. Rule of Complex Arithmetic

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5. ? = -tan?






6. Divide moduli and subtract arguments






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






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






9. Any number not rational






10. x / r






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






12. Given (4-2i) the complex conjugate would be (4+2i)






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






14. Equivalent to an Imaginary Unit.






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






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






17. Derives z = a+bi






18. To simplify a complex fraction






19. 5th. Rule of Complex Arithmetic






20. ½(e^(-y) +e^(y)) = cosh y






21. 1






22. Real and imaginary numbers






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






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






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






26. The field of all rational and irrational numbers.






27. A + bi






28. All the powers of i can be written as






29. No i






30. 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






31. 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






32. I






33. V(x² + y²) = |z|






34. Imaginary number

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






36. 1






37. 2a






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






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






40. The complex number z representing a+bi.






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

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42. Have radical






43. (e^(iz) - e^(-iz)) / 2i






44. 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






45. Like pi






46. The square root of -1.






47. 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.






48. E ^ (z2 ln z1)






49. y / r






50. z1z2* / |z2|²