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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • Match each statement with the correct term.
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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. 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






2. Root negative - has letter i






3. 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






4. y / r






5. I






6. (a + bi) = (c + bi) =






7. 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






8. 2ib






9. Where the curvature of the graph changes






10. Rotates anticlockwise by p/2






11. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






12. A + bi






13. 1






14. R?¹(cos? - isin?)






15. 3






16. V(x² + y²) = |z|






17. Starts at 1 - does not include 0






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

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19. 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.






20. Written as fractions - terminating + repeating decimals






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






22. Real and imaginary numbers






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






24. 1






25. (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






26. Numbers on a numberline






27. A complex number and its conjugate






28. ½(e^(-y) +e^(y)) = cosh y






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






30. z1z2* / |z2|²






31. A subset within a field.






32. When two complex numbers are multipiled together.






33. The square root of -1.






34. 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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35. ? = -tan?






36. E ^ (z2 ln z1)






37. Have radical






38. 3rd. Rule of Complex Arithmetic






39. Equivalent to an Imaginary Unit.






40. A+bi






41. 1






42. 2a






43. The reals are just the






44. The complex number z representing a+bi.






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

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46. Divide moduli and subtract arguments






47. To simplify a complex fraction






48. To simplify the square root of a negative number






49. Imaginary number

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