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






2. Where the curvature of the graph changes






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






4. Real and imaginary numbers






5. 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






6. 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






7. A plot of complex numbers as points.






8. 4th. Rule of Complex Arithmetic






9. Starts at 1 - does not include 0






10. To simplify a complex fraction






11. A complex number and its conjugate






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






13. 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.






14. 2a






15. All numbers






16. When two complex numbers are multipiled together.






17. 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


18. Numbers on a numberline






19. 2ib






20. (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






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






22. 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


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






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






25. V(x² + y²) = |z|






26. 1st. Rule of Complex Arithmetic






27. I^2 =






28. When you subtract two complex numbers a + bi and c + di - you get the difference of the real parts and the difference of the imaginary parts: (a + bi) - (c + di) = (a - c) + (b - d)i






29. 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






30. A+bi






31. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called






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. 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


34. Divide moduli and subtract arguments






35. Written as fractions - terminating + repeating decimals






36. I






37. E ^ (z2 ln z1)






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






39. ? = -tan?






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






41. No i






42. Any number not rational






43. 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






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






45. Rotates anticlockwise by p/2






46. Imaginary number

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


47. The reals are just the






48. Derives z = a+bi






49. 5th. Rule of Complex Arithmetic






50. Have radical