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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. (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






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






3. I






4. E ^ (z2 ln z1)






5. 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.






6. A subset within a field.






7. Numbers on a numberline






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






9. 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






10. Equivalent to an Imaginary Unit.






11. 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






12. 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






13. Have radical






14. All numbers






15. 2nd. Rule of Complex Arithmetic

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16. When two complex numbers are added together.






17. Multiply moduli and add arguments






18. A + bi






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






20. 3rd. Rule of Complex Arithmetic






21. To simplify the square root of a negative number






22. I






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






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






25. Root negative - has letter i






26. Written as fractions - terminating + repeating decimals






27. 1






28. Derives z = a+bi






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






30. 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.






31. Not on the numberline






32. 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






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






34. x / r






35. Any number not rational






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

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






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






39. R?¹(cos? - isin?)






40. ½(e^(-y) +e^(y)) = cosh y






41. We can also think of the point z= a+ ib as






42. 4th. Rule of Complex Arithmetic






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






44. When two complex numbers are multipiled together.






45. 1






46. All the powers of i can be written as






47. 2a






48. R^2 = x






49. A² + b² - real and non negative






50. To simplify a complex fraction