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






2. (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






3. x / r






4. A complex number and its conjugate






5. Derives z = a+bi






6. To simplify a complex fraction






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






8. Have radical






9. (2+i)(2i-3) you would use the foil methom which is first outter inner last. (2x2i)(2x-3)(ix2i^2)(ix(-3) =i-8






10. Multiply moduli and add arguments






11. 3rd. Rule of Complex Arithmetic






12. Equivalent to an Imaginary Unit.






13. I^2 =






14. ½(e^(iz) + e^(-iz))






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






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






17. Divide moduli and subtract arguments






18. A plot of complex numbers as points.






19. z1z2* / |z2|²






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






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






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






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






24. To simplify the square root of a negative number






25. 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






26. 1






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






28. Rotates anticlockwise by p/2






29. 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.'






30. 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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31. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






32. 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






33. 2a






34. All numbers






35. V(zz*) = v(a² + b²)






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






37. The square root of -1.






38. The product of an imaginary number and its conjugate is






39. 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






40. R?¹(cos? - isin?)






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






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






43. A² + b² - real and non negative






44. The complex number z representing a+bi.






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






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

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47. A + bi






48. Imaginary number

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49. A subset within a field.






50. Written as fractions - terminating + repeating decimals







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