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






2. 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.






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






4. 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






5. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






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


8. 3






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






10. 2nd. Rule of Complex Arithmetic


11. We consider the a real number x to be the complex number x+ 0i and in this way we can think of the real numbers as a subset of






12. 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






13. 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.'






14. 1






15. 2ib






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






17. 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






18. 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.






19. ½(e^(-y) +e^(y)) = cosh y






20. The square root of -1.






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






22. 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






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






24. 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.


25. 1






26. V(zz*) = v(a² + b²)






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






28. When two complex numbers are added together.






29. 4th. Rule of Complex Arithmetic






30. 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






31. Any number not rational






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






33. A + bi






34. Multiply moduli and add arguments






35. A subset within a field.






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






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






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






39. To simplify the square root of a negative number






40. Has exactly n roots by the fundamental theorem of algebra






41. I^2 =






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






43. ½(e^(iz) + e^(-iz))






44. E ^ (z2 ln z1)






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






46. When two complex numbers are multipiled together.






47. 1






48. Equivalent to an Imaginary Unit.






49. R^2 = x






50. 3rd. Rule of Complex Arithmetic