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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. 2ib






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






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






4. R?¹(cos? - isin?)






5. A plot of complex numbers as points.






6. Real and imaginary numbers






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






8. Root negative - has letter i






9. 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.






10. 1






11. The field of numbers of the form - where and are real numbers and i is the imaginary unit equal to the square root of - . When a single letter is used to denote a complex number - it is sometimes called an 'affix.'






12. z1z2* / |z2|²






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






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






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






16. Where the curvature of the graph changes






17. (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






18. Derives z = a+bi






19. I






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






21. x + iy = r(cos? + isin?) = re^(i?)






22. 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.






23. 1






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






25. 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






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






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






28. All numbers






29. 2a






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






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






32. ½(e^(iz) + e^(-iz))






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






34. 5th. Rule of Complex Arithmetic






35. R^2 = x






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






37. Not on the numberline






38. Like pi






39. 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






40. The square root of -1.






41. x / r






42. When two complex numbers are divided.






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






44. 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






45. 1






46. I^2 =






47. 3rd. Rule of Complex Arithmetic






48. (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






49. A+bi






50. y / r