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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. I






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






3. Equivalent to an Imaginary Unit.






4. When two complex numbers are divided.






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






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






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






8. 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






9. Written as fractions - terminating + repeating decimals






10. Not on the numberline






11. To simplify a complex fraction






12. To simplify the square root of a negative number






13. 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






14. 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.






15. All the powers of i can be written as






16. y / r






17. 1st. Rule of Complex Arithmetic






18. ? = -tan?






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






20. A + bi






21. 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.






22. (2i+3)/(9-i)for the denominator you multiply by the conjugate and what u do to the bottom u have to do to the top then you distribute the bottom then the top then add like terms then you simplify. 21i+25/17






23. Divide moduli and subtract arguments






24. 3






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






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






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






28. Rotates anticlockwise by p/2






29. Given (4-2i) the complex conjugate would be (4+2i)






30. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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

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






33. I






34. When two complex numbers are multipiled together.






35. 1






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






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






38. The reals are just the






39. 2ib






40. z1z2* / |z2|²






41. ½(e^(-y) +e^(y)) = cosh y






42. R^2 = x






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






44. I^2 =






45. xpressions such as ``the complex number z'' - and ``the point z'' are now






46. A plot of complex numbers as points.






47. (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






48. A² + b² - real and non negative






49. When two complex numbers are subtracted from one another.






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