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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • 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. 5th. Rule of Complex Arithmetic






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






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






4. 1






5. All the powers of i can be written as






6. 1






7. I






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


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. The square root of -1.






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






12. The reals are just the






13. ? = -tan?






14. 1






15. When two complex numbers are divided.






16. Real and imaginary numbers






17. Multiply moduli and add arguments






18. Rotates anticlockwise by p/2






19. 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






20. Not on the numberline






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






22. y / r






23. ½(e^(iz) + e^(-iz))






24. Numbers on a numberline






25. A+bi






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






27. Have radical






28. 3






29. Derives z = a+bi






30. All numbers






31. 2a






32. 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






33. Equivalent to an Imaginary Unit.






34. I






35. 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.






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






37. The field of all rational and irrational numbers.






38. R^2 = x






39. When two complex numbers are added together.






40. Divide moduli and subtract arguments






41. Starts at 1 - does not include 0






42. 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






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






44. 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.'






45. A + bi






46. A subset within a field.






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






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






49. To simplify a complex fraction






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