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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • 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. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n






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






3. Multiply moduli and add arguments






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






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






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






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






8. Like pi






9. A+bi






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






11. R?¹(cos? - isin?)






12. 3






13. When two complex numbers are divided.






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

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

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






17. Imaginary number

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18. ? = -tan?






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






20. z1z2* / |z2|²






21. All the powers of i can be written as






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






23. 1st. Rule of Complex Arithmetic






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






25. 1






26. I






27. A complex number and its conjugate






28. R^2 = x






29. 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






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






31. A plot of complex numbers as points.






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






33. ½(e^(-y) +e^(y)) = cosh y






34. 4th. Rule of Complex Arithmetic






35. 2ib






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. 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






38. 1






39. To simplify a complex fraction






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






41. Derives z = a+bi






42. 1






43. 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






44. Written as fractions - terminating + repeating decimals






45. Not on the numberline






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






47. Starts at 1 - does not include 0






48. 2a






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






50. A subset within a field.