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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. 1






2. 2ib






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

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4. Root negative - has letter i






5. Imaginary number

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6. A complex number and its conjugate






7. When two complex numbers are multipiled together.






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






9. 2a






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. ? = -tan?






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






13. I






14. 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






15. I






16. 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






17. All numbers






18. 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






19. 2nd. Rule of Complex Arithmetic

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






21. Real and imaginary numbers






22. 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






23. Not on the numberline






24. 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.






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






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






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






28. 1






29. Have radical






30. 1






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






32. 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.'






33. Multiply moduli and add arguments






34. To simplify a complex fraction






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






36. The square root of -1.






37. 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






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






39. Where the curvature of the graph changes






40. All the powers of i can be written as






41. Starts at 1 - does not include 0






42. Written as fractions - terminating + repeating decimals






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






44. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






45. ½(e^(-y) +e^(y)) = cosh y






46. A+bi






47. y / r






48. When two complex numbers are divided.






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






50. 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.