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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • 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. 2a






2. Equivalent to an Imaginary Unit.






3. Multiply moduli and add arguments






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






5. Imaginary number

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6. 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






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






8. 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






9. 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






10. x / r






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






12. To simplify the square root of a negative number






13. The complex number z representing a+bi.






14. 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






15. Starts at 1 - does not include 0






16. 5th. Rule of Complex Arithmetic






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






18. 4th. Rule of Complex Arithmetic






19. 1






20. 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.'






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






22. Like pi






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






24. Divide moduli and subtract arguments






25. I






26. 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






27. 3rd. Rule of Complex Arithmetic






28. ½(e^(iz) + e^(-iz))






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

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30. V(zz*) = v(a² + b²)






31. 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






32. 1






33. Rotates anticlockwise by p/2






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






35. I^2 =






36. R^2 = x






37. y / r






38. Written as fractions - terminating + repeating decimals






39. (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






40. 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.






41. To simplify a complex fraction






42. R?¹(cos? - isin?)






43. The reals are just the






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






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






46. 2ib






47. When two complex numbers are multipiled together.






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






49. A + bi






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






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