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






2. Real and imaginary numbers






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






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






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






6. We can also think of the point z= a+ ib as






7. The field of all rational and irrational numbers.






8. 2a






9. To simplify a complex fraction






10. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i






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






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

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13. ½(e^(-y) +e^(y)) = cosh y






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






15. 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






16. I^2 =






17. ? = -tan?






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






19. Multiply moduli and add arguments






20. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






21. 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






22. Rotates anticlockwise by p/2






23. When two complex numbers are multipiled together.






24. 1st. Rule of Complex Arithmetic






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






26. 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






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






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






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






30. 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.






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






32. A subset within a field.






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






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






35. The square root of -1.






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






37. (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






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






39. Not on the numberline






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






41. 1






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






43. All numbers






44. Numbers on a numberline






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

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46. Divide moduli and subtract arguments






47. 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.






48. V(x² + y²) = |z|






49. A + bi






50. 1







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