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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • 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. Any number not rational






2. 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






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






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






5. To simplify the square root of a negative number






6. Not on the numberline






7. 2nd. Rule of Complex Arithmetic

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8. R^2 = x






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

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10. 1






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






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






13. 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






14. (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






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






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






17. 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






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






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






20. The field of all rational and irrational numbers.






21. Imaginary number

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22. A number that cannot be expressed as a fraction for any integer.






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






24. A subset within a field.






25. x / r






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






27. 3






28. V(x² + y²) = |z|






29. 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






30. To simplify a complex fraction






31. Root negative - has letter i






32. Equivalent to an Imaginary Unit.






33. 1






34. No i






35. 1






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






37. 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






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

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39. 1






40. 1st. Rule of Complex Arithmetic






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






42. The square root of -1.






43. y / r






44. E ^ (z2 ln z1)






45. 5th. Rule of Complex Arithmetic






46. Rotates anticlockwise by p/2






47. 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.






48. Starts at 1 - does not include 0






49. Multiply moduli and add arguments






50. 1