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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. 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.'






2. To simplify the square root of a negative number






3. Rotates anticlockwise by p/2






4. 1






5. All the powers of i can be written as






6. 2ib






7. I






8. Starts at 1 - does not include 0






9. A subset within a field.






10. Real and imaginary numbers






11. A plot of complex numbers as points.






12. R?¹(cos? - isin?)






13. If z= a+bi is a complex number and a and b are real - we say that a is the real part of z and that b is the imaginary part of z






14. When two complex numbers are added together.






15. Where the curvature of the graph changes






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






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






18. Equivalent to an Imaginary Unit.






19. All numbers






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






21. y / r






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






23. ½(e^(-y) +e^(y)) = cosh y






24. 1st. Rule of Complex Arithmetic






25. A + bi






26. Have radical






27. The complex number z representing a+bi.






28. Root negative - has letter i






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

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30. 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






31. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






32. I^2 =






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






34. To simplify a complex fraction






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






36. 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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37. ? = -tan?






38. Any number not rational






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






40. 1






41. 1






42. 3rd. Rule of Complex Arithmetic






43. Written as fractions - terminating + repeating decimals






44. I






45. 1






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






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






48. Derives z = a+bi






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






50. (2+i)(2i-3) you would use the foil methom which is first outter inner last. (2x2i)(2x-3)(ix2i^2)(ix(-3) =i-8