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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. A subset within a field.






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

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3. 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






4. Where the curvature of the graph changes






5. ? = -tan?






6. When two complex numbers are divided.






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






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

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9. The reals are just the






10. 1






11. Like pi






12. Real and imaginary numbers






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






14. Equivalent to an Imaginary Unit.






15. 2a






16. ½(e^(iz) + e^(-iz))






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






18. 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






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






20. A+bi






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






22. Written as fractions - terminating + repeating decimals






23. 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






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






25. Have radical






26. The square root of -1.






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






28. All the powers of i can be written as






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






30. I^2 =






31. 2ib






32. 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.






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






34. Derives z = a+bi






35. V(x² + y²) = |z|






36. The complex number z representing a+bi.






37. To simplify the square root of a negative number






38. Not on the numberline






39. 1st. Rule of Complex Arithmetic






40. 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






41. ½(e^(-y) +e^(y)) = cosh y






42. 1. i^2 = -1 2. Every complex number has the 'Standard Form': a + bi for some real a and b. 3. For real a and b - a + bi = 0 if and only if a = b = 0 4. (a + bi) = (c + bi) = (a + c) + ( b + d)i 5. (a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc






43. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






44. 1






45. 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






46. Rotates anticlockwise by p/2






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






48. R^2 = x






49. E ^ (z2 ln z1)






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







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