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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • Match each statement with the correct term.
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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. Derives z = a+bi






3. A complex number and its conjugate






4. Real and imaginary numbers






5. 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






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






7. V(zz*) = v(a² + b²)






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






9. y / r






10. E ^ (z2 ln z1)






11. Any number not rational






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






13. ? = -tan?






14. ½(e^(iz) + e^(-iz))






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






16. (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






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

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






19. V(x² + y²) = |z|






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






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






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






23. A plot of complex numbers as points.






24. A + bi






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






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






27. All numbers






28. R^2 = x






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






30. When two complex numbers are multipiled together.






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






32. Multiply moduli and add arguments






33. 1






34. A subset within a field.






35. 3






36. Notice that rules 4 and 5 state that we complex numbers together - we can divide by c + di if c and d are not both zero. But there is a much easier way to do division.

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






38. When two complex numbers are divided.






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






40. When two complex numbers are subtracted from one another.






41. 3rd. Rule of Complex Arithmetic






42. To simplify a complex fraction






43. I






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






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






46. All the powers of i can be written as






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. 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.






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






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







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