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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^2 = x






2. A² + b² - real and non negative






3. The reals are just the






4. I






5. 4th. Rule of Complex Arithmetic






6. ? = -tan?






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






8. 3rd. Rule of Complex Arithmetic






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






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






11. 2nd. Rule of Complex Arithmetic

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12. 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.






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






14. 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






15. E ^ (z2 ln z1)






16. 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






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

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






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






20. 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






21. z1z2* / |z2|²






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






23. To simplify the square root of a negative number






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






25. 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.'






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






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






28. I






29. A + bi






30. No i






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






32. The field of all rational and irrational numbers.






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






34. Starts at 1 - does not include 0






35. Root negative - has letter i






36. Multiply moduli and add arguments






37. Have radical






38. A complex number and its conjugate






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

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40. Any number not rational






41. 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






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






43. 1st. Rule of Complex Arithmetic






44. y / r






45. 2a






46. Written as fractions - terminating + repeating decimals






47. R?¹(cos? - isin?)






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






49. 1






50. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i







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