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






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






4. 4th. Rule of Complex Arithmetic






5. Derives z = a+bi






6. The square root of -1.






7. We can also think of the point z= a+ ib as






8. 1






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

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10. No i






11. ½(e^(-y) +e^(y)) = cosh y






12. 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






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






14. Written as fractions - terminating + repeating decimals






15. Root negative - has letter i






16. Like pi






17. When two complex numbers are divided.






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






19. (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






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

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






22. ½(e^(iz) + e^(-iz))






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






24. The field of all rational and irrational numbers.






25. Numbers on a numberline






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






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






28. 5th. Rule of Complex Arithmetic






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






30. ? = -tan?






31. Real and imaginary numbers






32. A complex number and its conjugate






33. In the same way that we think of real numbers as being points on a line - it is natural to identify a complex number z=a+ib with the point (a -b) in the cartesian plane.






34. 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






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






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






37. A+bi






38. When two complex numbers are added together.






39. A plot of complex numbers as points.






40. Any number not rational






41. Rotates anticlockwise by p/2






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






43. A subset within a field.






44. Multiply moduli and add arguments






45. z1z2* / |z2|²






46. 3rd. Rule of Complex Arithmetic






47. E ^ (z2 ln z1)






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






49. Have radical






50. V(zz*) = v(a² + b²)