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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.
  • 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. 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






2. Have radical






3. 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.






4. Not on the numberline






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






6. Derives z = a+bi






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






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






9. Equivalent to an Imaginary Unit.






10. No i






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






12. Written as fractions - terminating + repeating decimals






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






14. 2nd. Rule of Complex Arithmetic

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






16. 1






17. x / r






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






19. Where the curvature of the graph changes






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






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






22. A+bi






23. I






24. The square root of -1.






25. 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






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






27. (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






28. Imaginary number

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29. 2a






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

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






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






33. 1






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






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






37. A² + b² - real and non negative






38. Any number not rational






39. Real and imaginary numbers






40. z1z2* / |z2|²






41. y / r






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






43. Rotates anticlockwise by p/2






44. 1






45. Numbers on a numberline






46. I^2 =






47. 1st. Rule of Complex Arithmetic






48. ½(e^(iz) + e^(-iz))






49. 3rd. Rule of Complex Arithmetic






50. V(x² + y²) = |z|