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






2. A subset within a field.






3. 1






4. Imaginary number

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






6. No i






7. The square root of -1.






8. 1st. Rule of Complex Arithmetic






9. When you subtract two complex numbers a + bi and c + di - you get the difference of the real parts and the difference of the imaginary parts: (a + bi) - (c + di) = (a - c) + (b - d)i






10. x / r






11. V(x² + y²) = |z|






12. 1






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

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14. To simplify a complex fraction






15. y / r






16. A plot of complex numbers as points.






17. I






18. z1z2* / |z2|²






19. Have radical






20. All the powers of i can be written as






21. All numbers






22. R?¹(cos? - isin?)






23. 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.






24. 4th. Rule of Complex Arithmetic






25. 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.






26. 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






27. To simplify the square root of a negative number






28. Equivalent to an Imaginary Unit.






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






30. ½(e^(-y) +e^(y)) = cosh y






31. Multiply moduli and add arguments






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






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






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






35. Derives z = a+bi






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






37. ½(e^(iz) + e^(-iz))






38. 5th. Rule of Complex Arithmetic






39. E ^ (z2 ln z1)






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






41. 1






42. I^2 =






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






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






45. 1






46. A + bi






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






48. Starts at 1 - does not include 0






49. When two complex numbers are added together.






50. 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







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