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. To simplify the square root of a negative number






2. Root negative - has letter i






3. (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






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






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






6. A + bi






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






8. The reals are just the






9. When two complex numbers are multipiled together.






10. I^2 =






11. 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






12. Derives z = a+bi






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






14. When two complex numbers are divided.






15. 3






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






17. All the powers of i can be written as






18. Like pi






19. 1






20. I






21. A subset within a field.






22. (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






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






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






25. 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






26. I






27. 1






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






29. The square root of -1.






30. 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


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






32. 2ib






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






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






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






36. 1






37. 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.






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






39. A complex number and its conjugate






40. When two complex numbers are added together.






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

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


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






43. 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.






44. A+bi






45. 1






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






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






48. 5th. Rule of Complex Arithmetic






49. Any number not rational






50. x / r