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. For real a and b - a + bi =






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


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






4. 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.






5. 2ib






6. A + bi






7. Divide moduli and subtract arguments






8. x / r






9. Not on the numberline






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






11. Root negative - has letter i






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






13. Numbers on a numberline






14. A+bi






15. Multiply moduli and add arguments






16. The complex number z representing a+bi.






17. Have radical






18. 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.


19. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






20. When two complex numbers are divided.






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






22. A complex number and its conjugate






23. To simplify the square root of a negative number






24. All numbers






25. 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.






26. Starts at 1 - does not include 0






27. 1






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


29. V(zz*) = v(a² + b²)






30. ½(e^(iz) + e^(-iz))






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






32. 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






33. 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






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






35. 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






36. R?¹(cos? - isin?)






37. 1






38. Derives z = a+bi






39. z1z2* / |z2|²






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






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






42. I






43. Where the curvature of the graph changes






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






45. The reals are just the






46. To prove that number field every algebraic equation in z with complex coefficients has a solution we need


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






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






49. 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






50. 1st. Rule of Complex Arithmetic