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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. 4th. Rule of Complex Arithmetic






2. A plot of complex numbers as points.






3. 1






4. Root negative - has letter i






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






6. Numbers on a numberline






7. Imaginary number

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8. ? = -tan?






9. I^2 =






10. 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






11. 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






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






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

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






15. The field of all rational and irrational numbers.






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






17. To simplify the square root of a negative number






18. 3






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






20. (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






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






22. 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






23. A subset within a field.






24. Derives z = a+bi






25. z1z2* / |z2|²






26. A complex number and its conjugate






27. R?¹(cos? - isin?)






28. 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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29. ½(e^(iz) + e^(-iz))






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






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






32. No i






33. Written as fractions - terminating + repeating decimals






34. Divide moduli and subtract arguments






35. Like pi






36. E ^ (z2 ln z1)






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






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






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






40. All the powers of i can be written as






41. Have radical






42. The square root of -1.






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






45. R^2 = x






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






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






48. 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.






49. 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.'






50. 2ib






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