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






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






3. ? = -tan?






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






5. The reals are just the






6. To simplify the square root of a negative number






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






8. V(x² + y²) = |z|






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






10. 1






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






12. 5th. Rule of Complex Arithmetic






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






14. 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






15. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






16. R?¹(cos? - isin?)






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






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






19. Not on the numberline






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






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






22. 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






23. z1z2* / |z2|²






24. Cos n? + i sin n? (for all n integers)






25. E^(i?) = cos? + isin? ; e^(ip) + 1 = 0

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






27. Like pi






28. ½(e^(-y) +e^(y)) = cosh y






29. Where the curvature of the graph changes






30. A complex number and its conjugate






31. Any number not rational






32. Starts at 1 - does not include 0






33. 1st. Rule of Complex Arithmetic






34. Equivalent to an Imaginary Unit.






35. Root negative - has letter i






36. 2a






37. 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.






38. A² + b² - real and non negative






39. ½(e^(iz) + e^(-iz))






40. When two complex numbers are multipiled together.






41. A+bi






42. 1






43. To simplify a complex fraction






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






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






46. R^2 = x






47. 1






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






49. 1






50. Rotates anticlockwise by p/2