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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. 1. i^2 = -1 2. Every complex number has the 'Standard Form': a + bi for some real a and b. 3. For real a and b - a + bi = 0 if and only if a = b = 0 4. (a + bi) = (c + bi) = (a + c) + ( b + d)i 5. (a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc






2. Not on the numberline






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






4. ½(e^(iz) + e^(-iz))






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






6. 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






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






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






9. ? = -tan?






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






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






12. 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






13. Where the curvature of the graph changes






14. 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.'






15. Real and imaginary numbers






16. Numbers on a numberline






17. E^(i?) = cos? + isin? ; e^(ip) + 1 = 0

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18. I






19. R?¹(cos? - isin?)






20. Any number not rational






21. Divide moduli and subtract arguments






22. A + bi






23. The complex number z representing a+bi.






24. 1st. Rule of Complex Arithmetic






25. The field of all rational and irrational numbers.






26. V(zz*) = v(a² + b²)






27. When two complex numbers are multipiled together.






28. All numbers






29. 2a






30. Written as fractions - terminating + repeating decimals






31. I






32. When two complex numbers are added together.






33. 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.






34. We consider the a real number x to be the complex number x+ 0i and in this way we can think of the real numbers as a subset of






35. Like pi






36. To simplify the square root of a negative number






37. A+bi






38. No i






39. A complex number may be taken to the power of another complex number.






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

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41. A plot of complex numbers as points.






42. Equivalent to an Imaginary Unit.






43. Root negative - has letter i






44. Multiply moduli and add arguments






45. Formula: z1 · z2 = (a + bi)(c + di) = ac +adi +cbi +bdi² = (ac - bd) + (ad +cb)i - when you multiply a complex number by its conjugate - you get a real number.






46. 2ib






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. z1z2* / |z2|²






49. y / r






50. I^2 =







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