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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. Where the curvature of the graph changes






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






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






4. 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.'






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

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






7. V(x² + y²) = |z|






8. A subset within a field.






9. All the powers of i can be written as






10. ½(e^(-y) +e^(y)) = cosh y






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

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12. A+bi






13. 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






14. Imaginary number

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






16. When two complex numbers are added together.






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






18. 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.






19. Derives z = a+bi






20. The square root of -1.






21. Equivalent to an Imaginary Unit.






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






23. Like pi






24. 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






25. Not on the numberline






26. R?¹(cos? - isin?)






27. To simplify a complex fraction






28. 2nd. Rule of Complex Arithmetic

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29. 3






30. 3rd. Rule of Complex Arithmetic






31. 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






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






33. Divide moduli and subtract arguments






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






35. I






36. ? = -tan?






37. Real and imaginary numbers






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






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






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






41. x / r






42. 1






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






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






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






46. All numbers






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






48. I^2 =






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






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