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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. R?¹(cos? - isin?)






2. Numbers on a numberline






3. Written as fractions - terminating + repeating decimals






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






5. The modulus of the complex number z= a + ib now can be interpreted as






6. The reals are just the






7. 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






8. The field of all rational and irrational numbers.






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






10. Multiply moduli and add arguments






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






12. Real and imaginary numbers






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

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14. 3rd. Rule of Complex Arithmetic






15. ½(e^(-y) +e^(y)) = cosh y






16. 2nd. Rule of Complex Arithmetic

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17. Root negative - has letter i






18. 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.






19. I^2 =






20. 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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21. 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






22. Have radical






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






24. Any number not rational






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






26. 4th. Rule of Complex Arithmetic






27. Equivalent to an Imaginary Unit.






28. Imaginary number

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29. A complex number and its conjugate






30. 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






31. No i






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






33. When two complex numbers are multipiled together.






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






35. When two complex numbers are divided.






36. A + bi






37. E ^ (z2 ln z1)






38. y / r






39. When two complex numbers are added together.






40. The complex number z representing a+bi.






41. A subset within a field.






42. x / r






43. 2ib






44. 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






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






46. A plot of complex numbers as points.






47. To simplify a complex fraction






48. V(zz*) = v(a² + b²)






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






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