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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. To simplify a complex fraction






2. I^2 =






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






4. We see in this way that the distance between two points z and w in the complex plane is






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






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






7. Multiply moduli and add arguments






8. The field of all rational and irrational numbers.






9. Have radical






10. Where the curvature of the graph changes






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






12. When two complex numbers are multipiled together.






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

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14. Written as fractions - terminating + repeating decimals






15. Root negative - has letter i






16. Imaginary number

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17. 5th. Rule of Complex Arithmetic






18. 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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19. Formula: z1 · z2 = (a + bi)(c + di) = ac +adi +cbi +bdi² = (ac - bd) + (ad +cb)i - when you multiply a complex number by its conjugate - you get a real number.






20. 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






21. A complex number may be taken to the power of another complex number.






22. 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






23. 1






24. I






25. A plot of complex numbers as points.






26. 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






27. All numbers






28. 1






29. 3rd. Rule of Complex Arithmetic






30. V(zz*) = v(a² + b²)






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

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32. 1st. Rule of Complex Arithmetic






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






34. ½(e^(-y) +e^(y)) = cosh y






35. z1z2* / |z2|²






36. 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






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






38. A + bi = z1 c + di = z2 - addition: z1 + z2 = (a + bi) + (c + di) = (a + c) + (b + d)i subtraction: z1 - z2 = (a - c) + (b - d)i






39. Divide moduli and subtract arguments






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






41. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






42. 2ib






43. The complex number z representing a+bi.






44. 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






45. 1






46. (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






47. A subset within a field.






48. 1






49. 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.






50. Numbers on a numberline