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






2. Rotates anticlockwise by p/2






3. E^(i?) = cos? + isin? ; e^(ip) + 1 = 0

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4. 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.






5. All the powers of i can be written as






6. 5th. Rule of Complex Arithmetic






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






8. 1






9. Divide moduli and subtract arguments






10. 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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11. Imaginary number

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12. 2nd. Rule of Complex Arithmetic

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13. The square root of -1.






14. x / r






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






16. ? = -tan?






17. 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.






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






19. A plot of complex numbers as points.






20. Starts at 1 - does not include 0






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






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






23. (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






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






25. 1






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

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27. 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






28. When two complex numbers are added together.






29. 1






30. A+bi






31. 3






32. Root negative - has letter i






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






34. z1z2* / |z2|²






35. To simplify the square root of a negative number






36. R^2 = x






37. y / r






38. I






39. 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






40. 3rd. Rule of Complex Arithmetic






41. 1






42. When two complex numbers are multipiled together.






43. A + bi






44. R?¹(cos? - isin?)






45. The field of all rational and irrational numbers.






46. I^2 =






47. When two complex numbers are divided.






48. V(x² + y²) = |z|






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






50. The complex number z representing a+bi.