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






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






3. ? = -tan?






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






5. All numbers






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






7. I






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






9. 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.






10. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






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






13. I^2 =






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






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






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






17. 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






18. E ^ (z2 ln z1)






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






20. I






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






22. 1






23. 3rd. Rule of Complex Arithmetic






24. Rotates anticlockwise by p/2






25. The field of all rational and irrational numbers.






26. 2a






27. 1






28. 1st. Rule of Complex Arithmetic






29. When two complex numbers are added together.






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






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






32. The field of numbers of the form - where and are real numbers and i is the imaginary unit equal to the square root of - . When a single letter is used to denote a complex number - it is sometimes called an 'affix.'






33. Numbers on a numberline






34. 1






35. A complex number and its conjugate






36. What about dividing one complex number by another? Is the result another complex number? Let's ask the question in another way. If you are given four real numbers a -b -c and d - can you find two other real numbers x and y so that






37. ½(e^(iz) + e^(-iz))






38. (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






39. Real and imaginary numbers






40. Imaginary number

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


41. V(zz*) = v(a² + b²)






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






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






44. 1






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






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






47. 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






48. Multiply moduli and add arguments






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






50. Derives z = a+bi