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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






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






3. No i






4. 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.'






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






6. 3






7. 2ib






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






9. Divide moduli and subtract arguments






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






11. 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






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






13. Imaginary number

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14. I






15. (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






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






17. Any number not rational






18. (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






19. x / r






20. 5th. Rule of Complex Arithmetic






21. 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.






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






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






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






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. ½(e^(iz) + e^(-iz))






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






28. 1






29. z1z2* / |z2|²






30. Written as fractions - terminating + repeating decimals






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






32. 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






33. 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






34. 1






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






36. A plot of complex numbers as points.






37. 1






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






40. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






42. Equivalent to an Imaginary Unit.






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






44. I






45. R^2 = x






46. The reals are just the






47. ? = -tan?






48. 1






49. A subset within a field.






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