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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. Like pi






2. When two complex numbers are divided.






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






4. 1st. Rule of Complex Arithmetic






5. 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






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






7. (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






8. The reals are just the






9. To simplify the square root of a negative number






10. 2a






11. All the powers of i can be written as






12. Numbers on a numberline






13. 1






14. The field of all rational and irrational numbers.






15. 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






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






17. 1






18. ½(e^(-y) +e^(y)) = cosh y






19. 2ib






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






21. A complex number and its conjugate






22. R^2 = x






23. Starts at 1 - does not include 0






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






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






26. Not on the numberline






27. Derives z = a+bi






28. 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






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






30. All numbers






31. 1






32. x / r






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






34. 5th. Rule of Complex Arithmetic






35. Written as fractions - terminating + repeating decimals






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






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






38. ? = -tan?






39. 1






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

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41. Equivalent to an Imaginary Unit.






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






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






44. 2nd. Rule of Complex Arithmetic

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45. Any number not rational






46. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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

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48. E ^ (z2 ln z1)






49. Rotates anticlockwise by p/2






50. V(zz*) = v(a² + b²)