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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. A subset within a field.






2. 1






3. When two complex numbers are added together.






4. 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






5. Written as fractions - terminating + repeating decimals






6. A + bi






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






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






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






10. 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.






11. 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






12. When you add two complex numbers a + bi and c + di - you get the sum of the real parts and the sum of the imaginary parts: (a + bi) + (c + di) = (a + c) + (b + d)i






13. 1






14. To prove that number field every algebraic equation in z with complex coefficients has a solution we need

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15. 2a






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






17. When two complex numbers are multipiled together.






18. R?¹(cos? - isin?)






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






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






21. ? = -tan?






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






23. Derives z = a+bi






24. 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.






25. The reals are just the






26. Multiply moduli and add arguments






27. 3






28. Like pi






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






30. I






31. E ^ (z2 ln z1)






32. R^2 = x






33. All numbers






34. 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






35. Numbers on a numberline






36. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






37. 1






38. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n






39. A complex number and its conjugate






40. 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






41. Equivalent to an Imaginary Unit.






42. Imaginary number

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






44. y / r






45. 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






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






47. Starts at 1 - does not include 0






48. ½(e^(iz) + e^(-iz))






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