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






2. A subset within a field.






3. 2a






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






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






6. 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






7. Like pi






8. I^2 =






9. Written as fractions - terminating + repeating decimals






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






11. 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.






12. R?¹(cos? - isin?)






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






14. Numbers on a numberline






15. Imaginary number

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16. Root negative - has letter i






17. 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






18. Starts at 1 - does not include 0






19. 1






20. The square root of -1.






21. The reals are just the






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






23. 1






24. What about dividing one complex number by another? Is the result another complex number? Let's ask the question in another way. If you are given four real numbers a -b -c and d - can you find two other real numbers x and y so that






25. E ^ (z2 ln z1)






26. The complex number z representing a+bi.






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






28. 4th. Rule of Complex Arithmetic






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






30. 1






31. 2nd. Rule of Complex Arithmetic

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32. A + bi = z1 c + di = z2 - addition: z1 + z2 = (a + bi) + (c + di) = (a + c) + (b + d)i subtraction: z1 - z2 = (a - c) + (b - d)i






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






34. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






35. When two complex numbers are multipiled together.






36. ½(e^(iz) + e^(-iz))






37. Real and imaginary numbers






38. z1z2* / |z2|²






39. Rotates anticlockwise by p/2






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






41. Where the curvature of the graph changes






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






43. Have radical






44. All numbers






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






46. When two complex numbers are added together.






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






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

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49. No i






50. To simplify the square root of a negative number