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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. The complex number z representing a+bi.






2. The field of all rational and irrational numbers.






3. To simplify a complex fraction






4. Multiply moduli and add arguments






5. Like pi






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






7. 1






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






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






10. Numbers on a numberline






11. ½(e^(-y) +e^(y)) = cosh y






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






13. Rotates anticlockwise by p/2






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






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






16. The product of an imaginary number and its conjugate is






17. A subset within a field.






18. 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






19. Starts at 1 - does not include 0






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






21. A + bi






22. When two complex numbers are multipiled together.






23. All the powers of i can be written as






24. 1st. Rule of Complex Arithmetic






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






26. y / r






27. No i






28. 3






29. 1






30. All numbers






31. A plot of complex numbers as points.






32. z1z2* / |z2|²






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






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






35. x / r






36. 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.






37. ½(e^(iz) + e^(-iz))






38. A complex number and its conjugate






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

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40. To simplify the square root of a negative number






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






42. (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






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






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






45. Have radical






46. R?¹(cos? - isin?)






47. Divide moduli and subtract arguments






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






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






50. 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