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






2. No i






3. xpressions such as ``the complex number z'' - and ``the point z'' are now






4. Multiply moduli and add arguments






5. To simplify the square root of a negative number






6. All the powers of i can be written as






7. The field of all rational and irrational numbers.






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






9. 3rd. Rule of Complex Arithmetic






10. 5th. Rule of Complex Arithmetic






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






12. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






14. 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






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






16. 1






17. The reals are just the






18. When two complex numbers are divided.






19. 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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20. Where the curvature of the graph changes






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

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






23. V(zz*) = v(a² + b²)






24. E ^ (z2 ln z1)






25. Any number not rational






26. 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






27. R^2 = x






28. Real and imaginary numbers






29. (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






30. A + bi






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






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






33. Derives z = a+bi






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






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






36. 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






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






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






39. A complex number and its conjugate






40. R?¹(cos? - isin?)






41. z1z2* / |z2|²






42. 1






43. 2a






44. The square root of -1.






45. 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.






46. ½(e^(-y) +e^(y)) = cosh y






47. A² + b² - real and non negative






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






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. Imaginary number

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