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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.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Every complex number has the 'Standard Form':






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






3. I^2 =






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






5. Any number not rational






6. (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






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






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






9. Rotates anticlockwise by p/2






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






11. Written as fractions - terminating + repeating decimals






12. Real and imaginary numbers






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






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






15. The square root of -1.






16. 1






17. Derives z = a+bi






18. 4th. Rule of Complex Arithmetic






19. 1






20. z1z2* / |z2|²






21. Starts at 1 - does not include 0






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

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






24. Multiply moduli and add arguments






25. 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.






26. All the powers of i can be written as






27. (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






28. 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






29. The field of all rational and irrational numbers.






30. When two complex numbers are multipiled together.






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






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






33. When two complex numbers are added together.






34. When you subtract two complex numbers a + bi and c + di - you get the difference of the real parts and the difference of the imaginary parts: (a + bi) - (c + di) = (a - c) + (b - d)i






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






36. A² + b² - real and non negative






37. Root negative - has letter i






38. Imaginary number

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






40. R?¹(cos? - isin?)






41. 2nd. Rule of Complex Arithmetic

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42. 2ib






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






44. ½(e^(-y) +e^(y)) = cosh y






45. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






46. No i






47. A complex number and its conjugate






48. A+bi






49. 1st. Rule of Complex Arithmetic






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