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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.
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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. I






2. Formula: z1 · z2 = (a + bi)(c + di) = ac +adi +cbi +bdi² = (ac - bd) + (ad +cb)i - when you multiply a complex number by its conjugate - you get a real number.






3. Starts at 1 - does not include 0






4. 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






5. When two complex numbers are multipiled together.






6. The complex number z representing a+bi.






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






8. y / r






9. 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






10. V(zz*) = v(a² + b²)






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

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12. Like pi






13. Root negative - has letter i






14. E ^ (z2 ln z1)






15. R?¹(cos? - isin?)






16. 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.






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






18. 1






19. 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






20. Have radical






21. Real and imaginary numbers






22. All the powers of i can be written as






23. 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






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






25. The reals are just the






26. Rotates anticlockwise by p/2






27. (e^(-y) - e^(y)) / 2i = i sinh y






28. The square root of -1.






29. x / r






30. Not on the numberline






31. E^(ln r) e^(i?) e^(2pin)






32. A + bi






33. When two complex numbers are divided.






34. (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






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






36. 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






37. Divide moduli and subtract arguments






38. Imaginary number

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39. To simplify the square root of a negative number






40. I






41. Multiply moduli and add arguments






42. A+bi






43. No i






44. A plot of complex numbers as points.






45. A² + b² - real and non negative






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






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






48. 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.






49. Written as fractions - terminating + repeating decimals






50. When two complex numbers are added together.