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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. 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






2. I






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






4. 5th. Rule of Complex Arithmetic






5. Not on the numberline






6. 2nd. Rule of Complex Arithmetic


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






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


9. Real and imaginary numbers






10. 4th. Rule of Complex Arithmetic






11. A+bi






12. 1






13. 1






14. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






16. 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






17. Equivalent to an Imaginary Unit.






18. Where the curvature of the graph changes






19. The field of all rational and irrational numbers.






20. The complex number z representing a+bi.






21. When two complex numbers are multipiled together.






22. A plot of complex numbers as points.






23. 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






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






25. R?¹(cos? - isin?)






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






27. 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.


28. 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.






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






30. The reals are just the






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






32. Numbers on a numberline






33. Rotates anticlockwise by p/2






34. (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






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






36. 2ib






37. 3rd. Rule of Complex Arithmetic






38. Divide moduli and subtract arguments






39. 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.






40. 1






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






42. ? = -tan?






43. ½(e^(iz) + e^(-iz))






44. 1






45. 3






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






47. 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.






48. 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






49. Starts at 1 - does not include 0






50. 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