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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. 3






2. ? = -tan?






3. Have radical






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






5. Imaginary number

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






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






8. 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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9. Where the curvature of the graph changes






10. When two complex numbers are divided.






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






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






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






14. Divide moduli and subtract arguments






15. z1z2* / |z2|²






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

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






18. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






19. y / r






20. Numbers on a numberline






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






22. V(x² + y²) = |z|






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






24. V(zz*) = v(a² + b²)






25. ½(e^(-y) +e^(y)) = cosh y






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






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

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28. 1






29. 2a






30. When two complex numbers are multipiled together.






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






32. To simplify a complex fraction






33. Starts at 1 - does not include 0






34. Multiply moduli and add arguments






35. Written as fractions - terminating + repeating decimals






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






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






38. The field of all rational and irrational numbers.






39. A plot of complex numbers as points.






40. 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






41. No i






42. 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.'






43. When two complex numbers are added together.






44. Any number not rational






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






46. 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






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






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






49. To simplify the square root of a negative number






50. 1