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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. 1






2. 2nd. Rule of Complex Arithmetic


3. A² + b² - real and non negative






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






5. V(zz*) = v(a² + b²)






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






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






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






9. R?¹(cos? - isin?)






10. Starts at 1 - does not include 0






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






12. R^2 = x






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






14. Not on the numberline






15. 2a






16. When two complex numbers are multipiled together.






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






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






19. Where the curvature of the graph changes






20. 3






21. 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






22. 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






23. 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.'






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






25. Real and imaginary numbers






26. Rotates anticlockwise by p/2






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






28. A + bi






29. To simplify the square root of a negative number






30. ½(e^(-y) +e^(y)) = cosh y






31. 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






32. 3rd. Rule of Complex Arithmetic






33. I






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






35. Root negative - has letter i






36. A+bi






37. When two complex numbers are divided.






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






39. 2ib






40. Any number not rational






41. (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






42. To simplify a complex fraction






43. (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






44. A number that can be expressed as a fraction p/q where q is not equal to 0.






45. ? = -tan?






46. Divide moduli and subtract arguments






47. 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






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






49. 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.






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