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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. A plot of complex numbers as points.






2. 3






3. (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






4. All numbers






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






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






7. When two complex numbers are divided.






8. Multiply moduli and add arguments






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

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10. A subset within a field.






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






12. I






13. 4th. Rule of Complex Arithmetic






14. I^2 =






15. No i






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






17. Not on the numberline






18. The field of all rational and irrational numbers.






19. V(x² + y²) = |z|






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






21. 1






22. Starts at 1 - does not include 0






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






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






25. V(zz*) = v(a² + b²)






26. 2nd. Rule of Complex Arithmetic

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27. Rotates anticlockwise by p/2






28. When two complex numbers are added together.






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






30. 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






31. 1






32. 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






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






34. 1






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






36. To simplify a complex fraction






37. Equivalent to an Imaginary Unit.






38. 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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39. For real a and b - a + bi =






40. To simplify the square root of a negative number






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






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






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






44. Real and imaginary numbers






45. Any number not rational






46. Written as fractions - terminating + repeating decimals






47. 3rd. Rule of Complex Arithmetic






48. 2ib






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






50. All the powers of i can be written as







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