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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. A plot of complex numbers as points.






2. 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.'






3. 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.






4. 1st. Rule of Complex Arithmetic






5. (2+i)(2i-3) you would use the foil methom which is first outter inner last. (2x2i)(2x-3)(ix2i^2)(ix(-3) =i-8






6. I






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






8. 5th. Rule of Complex Arithmetic






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

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






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






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






13. 3






14. 4th. Rule of Complex Arithmetic






15. 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






16. I = imaginary unit - i² = -1 or i = v-1






17. 3rd. Rule of Complex Arithmetic






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






19. Divide moduli and subtract arguments






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






21. Written as fractions - terminating + repeating decimals






22. 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.






23. No i






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






25. Rotates anticlockwise by p/2






26. V(x² + y²) = |z|






27. R^2 = x






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






29. The complex number z representing a+bi.






30. A + bi






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






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






33. Root negative - has letter i






34. When two complex numbers are multipiled together.






35. Any number not rational






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






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






38. A complex number and its conjugate






39. 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






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






41. 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






42. Have radical






43. 1






44. 2a






45. 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






46. All numbers






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






48. Not on the numberline






49. E ^ (z2 ln z1)






50. z1z2* / |z2|²







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