Test your basic knowledge |

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. Rotates anticlockwise by p/2






3. 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.






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






5. 3rd. Rule of Complex Arithmetic






6. Not on the numberline






7. 1






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






9. ½(e^(iz) + e^(-iz))






10. To simplify the square root of a negative number






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






12. (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






13. A subset within a field.






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






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






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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


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






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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


19. E ^ (z2 ln z1)






20. Where the curvature of the graph changes






21. 5th. Rule of Complex Arithmetic






22. To simplify a complex fraction






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






24. 1st. Rule of Complex Arithmetic






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. 1






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






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






29. 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






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






31. Real and imaginary numbers






32. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






33. Derives z = a+bi






34. Notice that rules 4 and 5 state that we complex numbers together - we can divide by c + di if c and d are not both zero. But there is a much easier way to do division.

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


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






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






37. The complex number z representing a+bi.






38. All numbers






39. 4th. Rule of Complex Arithmetic






40. 3






41. Equivalent to an Imaginary Unit.






42. A complex number and its conjugate






43. 2a






44. Imaginary number

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


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






46. Written as fractions - terminating + repeating decimals






47. 1






48. V(x² + y²) = |z|






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






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.