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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. x / r






2. Root negative - has letter i






3. y / r






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






5. R?¹(cos? - isin?)






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






7. 2a






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






10. Equivalent to an Imaginary Unit.






11. I^2 =






12. A + bi






13. (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






14. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






16. 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






17. A complex number and its conjugate






18. When two complex numbers are divided.






19. 2nd. Rule of Complex Arithmetic

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






21. (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






22. The field of all rational and irrational numbers.






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






24. A+bi






25. R^2 = x






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






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






28. ? = -tan?






29. When two complex numbers are added together.






30. 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






31. All numbers






32. Real and imaginary numbers






33. Imaginary number

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34. No i






35. Numbers on a numberline






36. Any number not rational






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






38. 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






39. I






40. The square root of -1.






41. 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






42. Rotates anticlockwise by p/2






43. 1






44. 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






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






46. Divide moduli and subtract arguments






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






48. Derives z = a+bi






49. Written as fractions - terminating + repeating decimals






50. ½(e^(-y) +e^(y)) = cosh y