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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. I






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






3. All the powers of i can be written as






4. Real and imaginary numbers






5. A subset within a field.






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






7. Divide moduli and subtract arguments






8. 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






9. A + bi






10. Imaginary number

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11. When two complex numbers are added together.






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






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






14. (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






15. A+bi






16. 2nd. Rule of Complex Arithmetic

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






18. R^2 = x






19. Have radical






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






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






22. R?¹(cos? - isin?)






23. Starts at 1 - does not include 0






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






25. Root negative - has letter i






26. V(x² + y²) = |z|






27. 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.






28. 1






29. Where the curvature of the graph changes






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






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






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






33. 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.






34. E ^ (z2 ln z1)






35. Multiply moduli and add arguments






36. 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.'






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






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






39. 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.






40. I






41. A plot of complex numbers as points.






42. 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






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






44. Written as fractions - terminating + repeating decimals






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






46. I^2 =






47. 1






48. The reals are just the






49. ½(e^(iz) + e^(-iz))






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