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






2. 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.






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






4. I






5. x / r






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






7. E^(i?) = cos? + isin? ; e^(ip) + 1 = 0

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8. 2nd. Rule of Complex Arithmetic

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






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






11. Where the curvature of the graph changes






12. A complex number and its conjugate






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






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






15. 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






16. To simplify the square root of a negative number






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






18. E ^ (z2 ln z1)






19. 1






20. Derives z = a+bi






21. R?¹(cos? - isin?)






22. 1st. Rule of Complex Arithmetic






23. 2a






24. Like pi






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






26. A subset within a field.






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






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






29. 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.






30. The complex number z representing a+bi.






31. 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






32. R^2 = x






33. 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






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






35. y / r






36. To simplify a complex fraction






37. A² + b² - real and non negative






38. A+bi






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






40. The square root of -1.






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

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42. A plot of complex numbers as points.






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






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






45. Starts at 1 - does not include 0






46. z1z2* / |z2|²






47. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1






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






49. 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.'






50. 5th. Rule of Complex Arithmetic