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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. Written as fractions - terminating + repeating decimals






2. (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






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






4. The field of numbers of the form - where and are real numbers and i is the imaginary unit equal to the square root of - . When a single letter is used to denote a complex number - it is sometimes called an 'affix.'






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






6. 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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7. 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






8. Rotates anticlockwise by p/2






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






10. x / r






11. All the powers of i can be written as






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






13. V(x² + y²) = |z|






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






15. 1






16. The field of all rational and irrational numbers.






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

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18. y / r






19. Root negative - has letter i






20. (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






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






22. z1z2* / |z2|²






23. 4th. Rule of Complex Arithmetic






24. 2nd. Rule of Complex Arithmetic

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






26. A subset within a field.






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






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






29. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....






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






31. 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.






32. Not on the numberline






33. 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






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






35. 3rd. Rule of Complex Arithmetic






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






37. All numbers






38. A+bi






39. Equivalent to an Imaginary Unit.






40. The reals are just the






41. Where the curvature of the graph changes






42. 3






43. 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.






44. 1






45. Starts at 1 - does not include 0






46. 1






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






48. A plot of complex numbers as points.






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

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50. 2a