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. z1z2* / |z2|²






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






3. 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.






4. Starts at 1 - does not include 0






5. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






7. A plot of complex numbers as points.






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






9. Any number not rational






10. If z= a+bi is a complex number and a and b are real - we say that a is the real part of z and that b is the imaginary part of z






11. I^2 =






12. 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.






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






14. Has exactly n roots by the fundamental theorem of algebra






15. 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.






16. Have radical






17. V(zz*) = v(a² + b²)






18. (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






19. R^2 = x






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






21. y / r






22. I






23. 1






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






25. Written as fractions - terminating + repeating decimals






26. 2nd. Rule of Complex Arithmetic

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


27. All numbers






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






29. Real and imaginary numbers






30. 3rd. Rule of Complex Arithmetic






31. 1






32. 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


33. The complex number z representing a+bi.






34. A complex number and its conjugate






35. 3






36. R?¹(cos? - isin?)






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






38. 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






39. 1






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






41. 2a






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






43. The reals are just the






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






45. No i






46. 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






47. When two complex numbers are added together.






48. The field of all rational and irrational numbers.






49. Like pi






50. A² + b² - real and non negative