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






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






3. Written as fractions - terminating + repeating decimals






4. I






5. I = imaginary unit - i² = -1 or i = v-1






6. When two complex numbers are divided.






7. 1st. Rule of Complex Arithmetic






8. 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






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






10. I^2 =






11. Imaginary number


12. Not on the numberline






13. 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.






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






15. 2a






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






17. A complex number and its conjugate






18. Real and imaginary numbers






19. 3rd. Rule of Complex Arithmetic






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






21. 3






22. Multiply moduli and add arguments






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


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






25. No i






26. ½(e^(iz) + e^(-iz))






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






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






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






30. 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.






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






32. ? = -tan?






33. y / r






34. 2ib






35. 1






36. Root negative - has letter i






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


38. All the powers of i can be written as






39. R?¹(cos? - isin?)






40. (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






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






42. A² + b² - real and non negative






43. To simplify a complex fraction






44. A subset within a field.






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






46. E ^ (z2 ln z1)






47. 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






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






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






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