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






2. 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






3. R^2 = x






4. All the powers of i can be written as






5. 1






6. Divide moduli and subtract arguments






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

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8. A plot of complex numbers as points.






9. The complex number z representing a+bi.






10. 2nd. Rule of Complex Arithmetic

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11. A + bi






12. Like pi






13. 1






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






15. Written as fractions - terminating + repeating decimals






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






17. V(zz*) = v(a² + b²)






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






19. 4th. Rule of Complex Arithmetic






20. The field of all rational and irrational numbers.






21. When two complex numbers are multipiled together.






22. 1






23. 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






24. 1






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






26. ? = -tan?






27. 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






28. Starts at 1 - does not include 0






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

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30. x / r






31. 3






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






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






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






35. 3rd. Rule of Complex Arithmetic






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






37. y / r






38. 1






39. Not on the numberline






40. We consider the a real number x to be the complex number x+ 0i and in this way we can think of the real numbers as a subset of






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

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






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






44. No i






45. To simplify the square root of a negative number






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






47. Where the curvature of the graph changes






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






49. I






50. Have radical