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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. 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.






2. The complex number z representing a+bi.






3. I^2 =






4. Root negative - has letter i






5. 4th. Rule of Complex Arithmetic






6. A subset within a field.






7. Multiply moduli and add arguments






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






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






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






11. Any number not rational






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






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






14. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






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






17. When two complex numbers are multipiled together.






18. A complex number and its conjugate






19. R?¹(cos? - isin?)






20. 1






21. x / r






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

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






24. 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.'






25. Divide moduli and subtract arguments






26. When two complex numbers are added together.






27. 2ib






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






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






30. Have radical






31. 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.






32. I






33. Derives z = a+bi






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






35. 1






36. When two complex numbers are divided.






37. No i






38. To simplify the square root of a negative number






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






40. To simplify a complex fraction






41. Real and imaginary numbers






42. 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






43. 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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44. A+bi






45. 2a






46. 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






47. A² + b² - real and non negative






48. 1






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

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