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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. Where the curvature of the graph changes






2. Multiply moduli and add arguments






3. 1






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






5. 2nd. Rule of Complex Arithmetic

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6. Like pi






7. A subset within a field.






8. To simplify the square root of a negative number






9. z1z2* / |z2|²






10. I






11. 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






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






13. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






15. 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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16. For real a and b - a + bi =






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






18. Numbers on a numberline






19. V(zz*) = v(a² + b²)






20. ½(e^(iz) + e^(-iz))






21. The square root of -1.






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






23. 2a






24. The field of all rational and irrational numbers.






25. Derives z = a+bi






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. 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






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






29. ? = -tan?






30. 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.'






31. R^2 = x






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






33. (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






34. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n






35. A + bi






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






37. 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






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






39. (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






40. 5th. Rule of Complex Arithmetic






41. 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.






42. 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






43. 1






44. Any number not rational






45. All the powers of i can be written as






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






47. Equivalent to an Imaginary Unit.






48. Imaginary number

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






50. A complex number and its conjugate