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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. Every complex number has the 'Standard Form':






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






3. x / r






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






5. The complex number z representing a+bi.






6. Divide moduli and subtract arguments






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






8. When two complex numbers are multipiled together.






9. The square root of -1.






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






11. 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.






12. 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.






13. y / r






14. 1






15. Where the curvature of the graph changes






16. ½(e^(iz) + e^(-iz))






17. E ^ (z2 ln z1)






18. The field of all rational and irrational numbers.






19. 5th. Rule of Complex Arithmetic






20. A complex number and its conjugate






21. I






22. Multiply moduli and add arguments






23. 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.






24. ? = -tan?






25. 4th. Rule of Complex Arithmetic






26. Imaginary number

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






28. 1st. Rule of Complex Arithmetic






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






30. The reals are just the






31. Real and imaginary numbers






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






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






34. z1z2* / |z2|²






35. 3






36. Numbers on a numberline






37. Written as fractions - terminating + repeating decimals






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






39. I^2 =






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

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41. Rotates anticlockwise by p/2






42. A + bi






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






44. V(x² + y²) = |z|






45. When two complex numbers are divided.






46. 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






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






48. A plot of complex numbers as points.






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






50. 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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