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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. Equivalent to an Imaginary Unit.






2. ½(e^(-y) +e^(y)) = cosh y






3. The reals are just the






4. 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






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






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






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






8. Where the curvature of the graph changes






9. When two complex numbers are divided.






10. Real and imaginary numbers






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






12. I






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






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






15. Imaginary number

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16. R^2 = x






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. For real a and b - a + bi =






19. (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






20. 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






21. No i






22. All the powers of i can be written as






23. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






24. 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






25. Divide moduli and subtract arguments






26. 2a






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






28. The square root of -1.






29. V(zz*) = v(a² + b²)






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






31. 1






32. V(x² + y²) = |z|






33. Have radical






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






35. (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






36. Not on the numberline






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






38. 1






39. A complex number and its conjugate






40. Any number not rational






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

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42. 1






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






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






45. Root negative - has letter i






46. To simplify a complex fraction






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






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






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. 2ib