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






2. To simplify the square root of a negative number






3. The reals are just the






4. R?¹(cos? - isin?)






5. 1






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






7. 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






8. Equivalent to an Imaginary Unit.






9. Derives z = a+bi






10. R^2 = x






11. 1






12. 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.






13. Have radical






14. z1z2* / |z2|²






15. A complex number and its conjugate






16. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






17. x / r






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






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






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






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






22. When two complex numbers are added together.






23. 3






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






25. (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






26. Not on the numberline






27. 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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28. Real and imaginary numbers






29. To simplify a complex fraction






30. A+bi






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






32. Written as fractions - terminating + repeating decimals






33. 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






34. A² + b² - real and non negative






35. No i






36. 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






37. 1






38. The field of all rational and irrational numbers.






39. y / r






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






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






42. A plot of complex numbers as points.






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






44. When two complex numbers are multipiled together.






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






46. I






47. Multiply moduli and add arguments






48. 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.'






49. I






50. Starts at 1 - does not include 0