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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. Have radical






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






3. I^2 =






4. To simplify the square root of a negative number






5. Written as fractions - terminating + repeating decimals






6. zn = (cos? + isin?)n = cosn? + isinn? - For all integers n

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7. 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






8. All the powers of i can be written as






9. E ^ (z2 ln z1)






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






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






12. Where the curvature of the graph changes






13. 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.

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14. ? = -tan?






15. A² + b² - real and non negative






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






17. A subset within a field.






18. R?¹(cos? - isin?)






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






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






21. 5th. Rule of Complex Arithmetic






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






23. Like pi






24. Rotates anticlockwise by p/2






25. 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






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






27. To simplify a complex fraction






28. Equivalent to an Imaginary Unit.






29. Starts at 1 - does not include 0






30. (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






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






32. z1z2* / |z2|²






33. y / r






34. Root negative - has letter i






35. 3






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






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






38. 2a






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






40. 1






41. V(zz*) = v(a² + b²)






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






43. 1






44. The reals are just the






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






46. 1






47. 2nd. Rule of Complex Arithmetic

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48. 1






49. A + bi






50. Derives z = a+bi