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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. For real a and b - a + bi =






2. 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.






3. Root negative - has letter i






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






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

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6. A² + b² - real and non negative






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






8. All the powers of i can be written as






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






10. A + bi






11. All numbers






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. ½(e^(-y) +e^(y)) = cosh y






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






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






16. 2ib






17. Divide moduli and subtract arguments






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






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






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






21. R^2 = x






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






23. Imaginary number

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






25. 4th. Rule of Complex Arithmetic






26. The square root of -1.






27. Like pi






28. 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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29. 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






30. 5th. Rule of Complex Arithmetic






31. Starts at 1 - does not include 0






32. Real and imaginary numbers






33. Where the curvature of the graph changes






34. Multiply moduli and add arguments






35. 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






36. A+bi






37. The reals are just the






38. Any number not rational






39. The complex number z representing a+bi.






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






41. ½(e^(iz) + e^(-iz))






42. z1z2* / |z2|²






43. A subset within a field.






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






45. A plot of complex numbers as points.






46. 2a






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






48. Derives z = a+bi






49. 2nd. Rule of Complex Arithmetic

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50. (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