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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. y / r






2. Root negative - has letter i






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






4. I






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






6. 3






7. 2nd. Rule of Complex Arithmetic

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8. Written as fractions - terminating + repeating decimals






9. All the powers of i can be written as






10. E^(i?) = cos? + isin? ; e^(ip) + 1 = 0

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11. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1






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






13. Multiply moduli and add arguments






14. R^2 = x






15. 4th. Rule of Complex Arithmetic






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






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






18. 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.






19. 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






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






21. 1






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






23. 1






24. The field of all rational and irrational numbers.






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






26. 3rd. Rule of Complex Arithmetic






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






28. Derives z = a+bi






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






30. Starts at 1 - does not include 0






31. (2i+3)/(9-i)for the denominator you multiply by the conjugate and what u do to the bottom u have to do to the top then you distribute the bottom then the top then add like terms then you simplify. 21i+25/17






32. 1






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






34. x / r






35. 1st. Rule of Complex Arithmetic






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

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37. Like pi






38. R?¹(cos? - isin?)






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






40. 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.'






41. ½(e^(iz) + e^(-iz))






42. 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






43. 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






44. I






45. The square root of -1.






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






47. When two complex numbers are multipiled together.






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






49. Any number not rational






50. The complex number z representing a+bi.