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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. 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.






2. 5th. Rule of Complex Arithmetic






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






4. Written as fractions - terminating + repeating decimals






5. R?¹(cos? - isin?)






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






7. All numbers






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






9. 2ib






10. Rotates anticlockwise by p/2






11. 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






12. I






13. R^2 = x






14. A² + b² - real and non negative






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






16. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






18. 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






19. y / r






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






21. Any number not rational






22. All the powers of i can be written as






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






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






25. z1z2* / |z2|²






26. Equivalent to an Imaginary Unit.






27. A plot of complex numbers as points.






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






29. 1






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






31. 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.'






32. ? = -tan?






33. I^2 =






34. Like pi






35. The reals are just the






36. 4th. Rule of Complex Arithmetic






37. The square root of -1.






38. x / r






39. 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






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






41. I






42. A complex number and its conjugate






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






44. A subset within a field.






45. 1






46. (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






47. Multiply moduli and add arguments






48. The field of all rational and irrational numbers.






49. Real and imaginary numbers






50. Not on the numberline