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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • 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. All the powers of i can be written as






2. 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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3. When two complex numbers are multipiled together.






4. 2a






5. 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.






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






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






8. Written as fractions - terminating + repeating decimals






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






10. 2ib






11. Solutions to zn = 1 - |z| = 1 - z = e^(i?) - e^(in?) = 1






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






13. Real and imaginary numbers






14. Derives z = a+bi






15. No i






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






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

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18. I^2 =






19. R^2 = x






20. 1






21. 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.






22. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






23. z1z2* / |z2|²






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






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






26. 3rd. Rule of Complex Arithmetic






27. A² + b² - real and non negative






28. To simplify a complex fraction






29. The reals are just the






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






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






32. When two complex numbers are added together.






33. 1






34. 5th. Rule of Complex Arithmetic






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






36. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i






37. All numbers






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






39. V(zz*) = v(a² + b²)






40. A + bi






41. 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






42. Starts at 1 - does not include 0






43. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....






44. A subset within a field.






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






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






47. The field of all rational and irrational numbers.






48. Have radical






49. (2i+3)/(9-i)for the denominator you multiply by the conjugate and what u do to the bottom u have to do to the top then you distribute the bottom then the top then add like terms then you simplify. 21i+25/17






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