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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. The field of all rational and irrational numbers.






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






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






4. When two complex numbers are divided.






5. E ^ (z2 ln z1)






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






7. 3






8. A+bi






9. 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.






10. A² + b² - real and non negative






11. Starts at 1 - does not include 0






12. No i






13. ½(e^(iz) + e^(-iz))






14. Numbers on a numberline






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






16. 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






17. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i






18. Equivalent to an Imaginary Unit.






19. Multiply moduli and add arguments






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






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






22. V(zz*) = v(a² + b²)






23. ½(e^(-y) +e^(y)) = cosh y






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






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






26. Any number not rational






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






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






29. 1






30. The reals are just the






31. Have radical






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






33. 2ib






34. The complex number z representing a+bi.






35. R^2 = x






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






37. A subset within a field.






38. I






39. Rotates anticlockwise by p/2






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






41. 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.'






42. 1






43. (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






44. 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






45. 1






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






47. 2nd. Rule of Complex Arithmetic


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






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






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