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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. When two complex numbers are divided.






2. A² + b² - real and non negative






3. 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






4. I^2 =






5. A + bi






6. Starts at 1 - does not include 0






7. ½(e^(-y) +e^(y)) = cosh y






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






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






10. Written as fractions - terminating + repeating decimals






11. When two complex numbers are added together.






12. ? = -tan?






13. zn = (cos? + isin?)n = cosn? + isinn? - For all integers n

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14. 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






15. V(zz*) = v(a² + b²)






16. E ^ (z2 ln z1)






17. Imaginary number

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18. 1






19. 1






20. z1z2* / |z2|²






21. No i






22. y / r






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






24. 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






25. V(x² + y²) = |z|






26. 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.






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






28. The reals are just the






29. I






30. Derives z = a+bi






31. Numbers on a numberline






32. Divide moduli and subtract arguments






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






34. Not on the numberline






35. 1st. Rule of Complex Arithmetic






36. A plot of complex numbers as points.






37. x + iy = r(cos? + isin?) = re^(i?)






38. Real and imaginary numbers






39. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n






40. Where the curvature of the graph changes






41. R?¹(cos? - isin?)






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






43. Notice that rules 4 and 5 state that we complex numbers together - we can divide by c + di if c and d are not both zero. But there is a much easier way to do division.

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44. 3






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






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






47. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






49. 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.






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