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






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






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






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






5. z1z2* / |z2|²






6. y / r






7. 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






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






9. When two complex numbers are multipiled together.






10. V(zz*) = v(a² + b²)






11. 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






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






13. 1






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

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15. To simplify the square root of a negative number






16. 5th. Rule of Complex Arithmetic






17. All numbers






18. E ^ (z2 ln z1)






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






20. A plot of complex numbers as points.






21. Not on the numberline






22. V(x² + y²) = |z|






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






24. 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.






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






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






27. A subset within a field.






28. R^2 = x






29. If z= a+bi is a complex number and a and b are real - we say that a is the real part of z and that b is the imaginary part of z






30. 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.






31. 1






32. Where the curvature of the graph changes






33. Root negative - has letter i






34. When two complex numbers are added together.






35. Rotates anticlockwise by p/2






36. 3






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






38. 2ib






39. A complex number and its conjugate






40. 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






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






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

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43. 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.'






44. Real and imaginary numbers






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






46. Multiply moduli and add arguments






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






48. A+bi






49. A + bi






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