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. ½(e^(-y) +e^(y)) = cosh y






2. V(x² + y²) = |z|






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 number not rational






5. 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.






6. To simplify the square root of a negative number






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






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






9. 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






10. Derives z = a+bi






11. E ^ (z2 ln z1)






12. 1






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






14. x / r






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






16. 1






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






18. A plot of complex numbers as points.






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






20. I






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






22. The field of all rational and irrational numbers.






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






24. R^2 = x






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






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






27. When two complex numbers are multipiled together.






28. 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.






29. 1






30. When two complex numbers are added together.






31. 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






32. (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






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






34. Like pi






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






36. 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






37. 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






38. 5th. Rule of Complex Arithmetic






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






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






41. To simplify a complex fraction






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






43. 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


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






45. 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.'






46. Where the curvature of the graph changes






47. A+bi






48. Notice that rules 4 and 5 state that we complex numbers together - we can divide by c + di if c and d are not both zero. But there is a much easier way to do division.

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


49. 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.






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