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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. y / r






2. 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.






3. 3






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






5. 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






6. Cos n? + i sin n? (for all n integers)






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






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






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






10. R^2 = x






11. When two complex numbers are divided.






12. Like pi






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






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






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






16. R?¹(cos? - isin?)






17. A + bi






18. I^2 =






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






20. Divide moduli and subtract arguments






21. 2a






22. ½(e^(-y) +e^(y)) = cosh y






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






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

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25. No i






26. Not on the numberline






27. 2ib






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

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29. Written as fractions - terminating + repeating decimals






30. Real and imaginary numbers






31. (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






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






33. To simplify a complex fraction






34. A complex number and its conjugate






35. 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.






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






37. All numbers






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






39. To simplify the square root of a negative number






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






41. 1






42. Imaginary number

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43. All the powers of i can be written as






44. 1






45. Derives z = a+bi






46. Numbers on a numberline






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






48. E ^ (z2 ln z1)






49. If z= a+bi is a complex number and a and b are real - we say that a is the real part of z and that b is the imaginary part of z






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