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. 4th. Rule of Complex Arithmetic






2. 1






3. Divide moduli and subtract arguments






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






5. Not on the numberline






6. 1






7. ? = -tan?






8. 1






9. 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






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






11. A plot of complex numbers as points.






12. Rotates anticlockwise by p/2






13. I






14. V(zz*) = v(a² + b²)






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






16. 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.'






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






18. 1st. Rule of Complex Arithmetic






19. 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






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






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






22. To simplify a complex fraction






23. No i






24. 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.






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






26. I






27. V(x² + y²) = |z|






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






29. The field of all rational and irrational numbers.






30. The square root of -1.






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






32. When two complex numbers are added together.






33. (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






34. Where the curvature of the graph changes






35. A subset within a field.






36. A+bi






37. ½(e^(iz) + e^(-iz))






38. A + bi






39. Any number not rational






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






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






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






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






44. Imaginary number


45. A² + b² - real and non negative






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






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






48. Numbers on a numberline






49. Root negative - has letter i






50. 2ib