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






2. A+bi






3. Equivalent to an Imaginary Unit.






4. A subset within a field.






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






6. A complex number and its conjugate






7. 1






8. To simplify a complex fraction






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






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






11. R^2 = x






12. 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






13. 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.






14. Divide moduli and subtract arguments






15. Numbers on a numberline






16. Any number not rational






17. Any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.






18. (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






19. Written as fractions - terminating + repeating decimals






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






21. ½(e^(-y) +e^(y)) = cosh y






22. The square root of -1.






23. Not on the numberline






24. Starts at 1 - does not include 0






25. 1






26. 1






27. No i






28. 1






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






30. (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






31. A + bi






32. 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






33. 1






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






35. 3rd. Rule of Complex Arithmetic






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






37. 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.






38. ½(e^(iz) + e^(-iz))






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






40. ? = -tan?






41. V(x² + y²) = |z|






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

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43. 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






44. A plot of complex numbers as points.






45. V(zz*) = v(a² + b²)






46. To simplify the square root of a negative number






47. 2nd. Rule of Complex Arithmetic

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48. E ^ (z2 ln z1)






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






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