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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. Rotates anticlockwise by p/2






2. y / r






3. x / r






4. 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






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






6. A + bi






7. 2nd. Rule of Complex Arithmetic

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






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






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






11. 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






12. Starts at 1 - does not include 0






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






14. 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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15. 1






16. 1






17. z1z2* / |z2|²






18. ? = -tan?






19. The reals are just the






20. Root negative - has letter i






21. All numbers






22. A subset within a field.






23. Numbers on a numberline






24. 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






25. ½(e^(iz) + e^(-iz))






26. 5th. Rule of Complex Arithmetic






27. I^2 =






28. Not on the numberline






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






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






31. (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






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






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






34. 1






35. All the powers of i can be written as






36. 2ib






37. Written as fractions - terminating + repeating decimals






38. (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






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






40. No i






41. Equivalent to an Imaginary Unit.






42. A complex number may be taken to the power of another complex number.






43. Real and imaginary numbers






44. To simplify the square root of a negative number






45. 1






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






47. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






48. 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.






49. Multiply moduli and add arguments






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