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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. Multiply moduli and add arguments






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






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






4. 1






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

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






7. The square root of -1.






8. A complex number and its conjugate






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






10. We consider the a real number x to be the complex number x+ 0i and in this way we can think of the real numbers as a subset of






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

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12. Derives z = a+bi






13. 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.






14. y / r






15. 1






16. 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.






17. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






18. Divide moduli and subtract arguments






19. No i






20. A subset within a field.






21. 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.






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






23. 1st. Rule of Complex Arithmetic






24. Where the curvature of the graph changes






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






26. ? = -tan?






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






28. Rotates anticlockwise by p/2






29. Have radical






30. Given (4-2i) the complex conjugate would be (4+2i)






31. 2a






32. Not on the numberline






33. Written as fractions - terminating + repeating decimals






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






35. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1






36. 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






37. I






38. V(x² + y²) = |z|






39. ½(e^(-y) +e^(y)) = cosh y






40. Numbers on a numberline






41. When two complex numbers are divided.






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. To simplify the square root of a negative number






44. 1






45. 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






46. Like pi






47. Starts at 1 - does not include 0






48. A² + b² - real and non negative






49. The field of all rational and irrational numbers.






50. A + bi