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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. I^2 =






2. 1






3. 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






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






5. ½(e^(-y) +e^(y)) = cosh y






6. Divide moduli and subtract arguments






7. Numbers on a numberline






8. 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.






9. The reals are just the






10. Real and imaginary numbers






11. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






13. x / r






14. 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






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






16. I






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






18. A complex number and its conjugate






19. ? = -tan?






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






21. 1






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






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

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24. y / r






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






26. The field of numbers of the form - where and are real numbers and i is the imaginary unit equal to the square root of - . When a single letter is used to denote a complex number - it is sometimes called an 'affix.'






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






28. R?¹(cos? - isin?)






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






30. 2ib






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






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






34. A plot of complex numbers as points.






35. 4th. Rule of Complex Arithmetic






36. Derives z = a+bi






37. 2a






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






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






40. (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






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






42. Rotates anticlockwise by p/2






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






44. No i






45. A subset within a field.






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






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






48. A² + b² - real and non negative






49. ½(e^(iz) + e^(-iz))






50. Not on the numberline