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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. Any number not rational






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. z1z2* / |z2|²






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






5. The field of all rational and irrational numbers.






6. Real and imaginary numbers






7. 1st. Rule of Complex Arithmetic






8. 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






9. Divide moduli and subtract arguments






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






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






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

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






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






15. 1






16. ½(e^(iz) + e^(-iz))






17. 4th. Rule of Complex Arithmetic






18. Written as fractions - terminating + repeating decimals






19. 5th. Rule of Complex Arithmetic






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






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






22. 3rd. Rule of Complex Arithmetic






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






24. A complex number and its conjugate






25. 2ib






26. The reals are just the






27. V(zz*) = v(a² + b²)






28. Equivalent to an Imaginary Unit.






29. Imaginary number

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30. No i






31. ? = -tan?






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






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






34. Where the curvature of the graph changes






35. 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.'






36. 2nd. Rule of Complex Arithmetic

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






38. (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






39. I^2 =






40. R^2 = x






41. ½(e^(-y) +e^(y)) = cosh y






42. 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






43. Formula: z1 · z2 = (a + bi)(c + di) = ac +adi +cbi +bdi² = (ac - bd) + (ad +cb)i - when you multiply a complex number by its conjugate - you get a real number.






44. 2a






45. V(x² + y²) = |z|






46. 1






47. 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






48. All numbers






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






50. y / r







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