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






2. 1






3. 4th. Rule of Complex Arithmetic






4. A + bi






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






6. I^26/4= i^24 x i^2 =-1 so u divide the number by 4 and whatevers left over is the number that its equal to.






7. Multiply moduli and add arguments






8. When two complex numbers are multipiled together.






9. Any number not rational






10. The reals are just the






11. Numbers on a numberline






12. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i






13. I






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

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






16. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






17. Root negative - has letter i






18. Equivalent to an Imaginary Unit.






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






20. 1






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






22. 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






23. (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






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






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






26. 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






27. V(x² + y²) = |z|






28. Starts at 1 - does not include 0






29. All the powers of i can be written as






30. The complex number z representing a+bi.






31. I






32. R?¹(cos? - isin?)






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

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34. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called






35. 3rd. Rule of Complex Arithmetic






36. 5th. Rule of Complex Arithmetic






37. R^2 = x






38. Divide moduli and subtract arguments






39. V(zz*) = v(a² + b²)






40. A² + b² - real and non negative






41. Real and imaginary numbers






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






43. No i






44. 1






45. To simplify the square root of a negative number






46. A plot of complex numbers as points.






47. Not on the numberline






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






49. Written as fractions - terminating + repeating decimals






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

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