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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.
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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. The square root of -1.






3. Real and imaginary numbers






4. Rotates anticlockwise by p/2






5. 3






6. 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






7. x / r






8. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






9. Multiply moduli and add arguments






10. 1






11. The reals are just the






12. 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.






13. R^2 = x






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






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






16. R?¹(cos? - isin?)






17. V(zz*) = v(a² + b²)






18. All the powers of i can be written as






19. Starts at 1 - does not include 0






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






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






22. Not on the numberline






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






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






25. To simplify the square root of a negative number






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






27. 1






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






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






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






31. When two complex numbers are divided.






32. I






33. When two complex numbers are multipiled together.






34. A+bi






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






36. ½(e^(iz) + e^(-iz))






37. 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






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






39. 4th. Rule of Complex Arithmetic






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






41. 1






42. Written as fractions - terminating + repeating decimals






43. I






44. To simplify a complex fraction






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






46. 1






47. 1st. Rule of Complex Arithmetic






48. Derives z = a+bi






49. 2a






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

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