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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 complex number and its conjugate






2. 4th. Rule of Complex Arithmetic






3. No i






4. 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.






5. Notice that rules 4 and 5 state that we complex numbers together - we can divide by c + di if c and d are not both zero. But there is a much easier way to do division.

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6. 5th. Rule of Complex Arithmetic






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






8. 2nd. Rule of Complex Arithmetic

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9. Numbers on a numberline






10. All the powers of i can be written as






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






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






13. Where the curvature of the graph changes






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






15. V(x² + y²) = |z|






16. 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






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






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






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






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






21. R^2 = x






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






23. (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






24. 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






25. Real and imaginary numbers






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






27. Root negative - has letter i






28. Multiply moduli and add arguments






29. y / r






30. 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






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






32. ½(e^(-y) +e^(y)) = cosh y






33. E ^ (z2 ln z1)






34. 1st. Rule of Complex Arithmetic






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






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






37. Like pi






38. Starts at 1 - does not include 0






39. Not on the numberline






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






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






42. 1






43. A² + b² - real and non negative






44. The field of all rational and irrational numbers.






45. I






46. (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






47. I






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






49. ? = -tan?






50. 2a







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