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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. All the powers of i can be written as






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






3. 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.'






4. 1






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

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6. 5th. Rule of Complex Arithmetic






7. Root negative - has letter i






8. All numbers






9. 3






10. V(zz*) = v(a² + b²)






11. 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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12. No i






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






14. 4th. Rule of Complex Arithmetic






15. Any number not rational






16. V(x² + y²) = |z|






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






18. Divide moduli and subtract arguments






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






20. Real and imaginary numbers






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






22. R^2 = x






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






24. Not on the numberline






25. 1






26. ? = -tan?






27. x / r






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






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






30. 2ib






31. 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






32. Written as fractions - terminating + repeating decimals






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






34. A² + b² - real and non negative






35. 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






36. A+bi






37. To simplify a complex fraction






38. E ^ (z2 ln z1)






39. A plot of complex numbers as points.






40. Multiply moduli and add arguments






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






42. 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






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






44. 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






45. R?¹(cos? - isin?)






46. 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.






47. ½(e^(-y) +e^(y)) = cosh y






48. I






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






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