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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. Divide moduli and subtract arguments






2. R^2 = x






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






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






5. V(x² + y²) = |z|






6. 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.






7. 1






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






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






10. (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






11. 3rd. Rule of Complex Arithmetic






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






13. I^2 =






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






15. A subset within a field.






16. Multiply moduli and add arguments






17. Where the curvature of the graph changes






18. 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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19. The complex number z representing a+bi.






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






21. ½(e^(iz) + e^(-iz))






22. (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






23. Written as fractions - terminating + repeating decimals






24. ? = -tan?






25. 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






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






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

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28. 4th. Rule of Complex Arithmetic






29. 1






30. When two complex numbers are divided.






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






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






33. Starts at 1 - does not include 0






34. A + bi






35. 2a






36. E ^ (z2 ln z1)






37. 1st. Rule of Complex Arithmetic






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






39. Any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.






40. What about dividing one complex number by another? Is the result another complex number? Let's ask the question in another way. If you are given four real numbers a -b -c and d - can you find two other real numbers x and y so that






41. Real and imaginary numbers






42. A+bi






43. 1






44. A complex number and its conjugate






45. I






46. 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






47. z1z2* / |z2|²






48. 2nd. Rule of Complex Arithmetic

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






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






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