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






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






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






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






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






6. R^2 = x






7. In this amazing number field every algebraic equation in z with complex coefficients






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






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






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






12. A subset within a field.






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






14. Root negative - has letter i






15. 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.'






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. 1






18. I = imaginary unit - i² = -1 or i = v-1






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






20. 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






21. 1






22. 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






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






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






25. The reals are just the






26. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






27. Where the curvature of the graph changes






28. E ^ (z2 ln z1)






29. 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






30. Any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.






31. I






32. The square root of -1.






33. A² + b² - real and non negative






34. Written as fractions - terminating + repeating decimals






35. 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.






36. Real and imaginary numbers






37. 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






38. Multiply moduli and add arguments






39. ½(e^(-y) +e^(y)) = cosh y






40. Derives z = a+bi






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






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






43. ½(e^(iz) + e^(-iz))






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

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45. 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






46. Equivalent to an Imaginary Unit.






47. R?¹(cos? - isin?)






48. When two complex numbers are divided.






49. (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






50. To simplify a complex fraction