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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. E ^ (z2 ln z1)






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






4. Derives z = a+bi






5. y / r






6. When two complex numbers are multipiled together.






7. The complex number z representing a+bi.






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






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






10. Root negative - has letter i






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






12. Any number not rational






13. 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






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






15. V(x² + y²) = |z|






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






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






18. E^(ln r) e^(i?) e^(2pin)






19. R^2 = x






20. 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.






21. 1






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

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23. A subset within a field.






24. (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






25. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






26. Equivalent to an Imaginary Unit.






27. The field of all rational and irrational numbers.






28. A² + b² - real and non negative






29. z1z2* / |z2|²






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. Have radical






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

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33. Rotates anticlockwise by p/2






34. The reals are just the






35. No i






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






37. Not on the numberline






38. 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






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






40. 1






41. Where the curvature of the graph changes






42. 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.






43. 1






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






45. 2ib






46. ½(e^(iz) + e^(-iz))






47. Numbers on a numberline






48. 1. i^2 = -1 2. Every complex number has the 'Standard Form': a + bi for some real a and b. 3. For real a and b - a + bi = 0 if and only if a = b = 0 4. (a + bi) = (c + bi) = (a + c) + ( b + d)i 5. (a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc






49. R?¹(cos? - isin?)






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







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