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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. 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






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






3. Real and imaginary numbers






4. 3rd. Rule of Complex Arithmetic






5. When two complex numbers are multipiled together.






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






7. Numbers on a numberline






8. Where the curvature of the graph changes






9. 3






10. Multiply moduli and add arguments






11. A + bi






12. Starts at 1 - does not include 0






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






14. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






16. Root negative - has letter i






17. (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






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






19. E ^ (z2 ln z1)






20. ? = -tan?






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

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22. A complex number and its conjugate






23. When two complex numbers are added together.






24. 2nd. Rule of Complex Arithmetic

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25. 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






26. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.






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






28. 1






29. A² + b² - real and non negative






30. Derives z = a+bi






31. When two complex numbers are divided.






32. Any number not rational






33. A subset within a field.






34. 1






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






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






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






38. 1






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

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40. Like pi






41. x / r






42. All the powers of i can be written as






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

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44. 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






45. 1






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






47. The square root of -1.






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






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






50. Written as fractions - terminating + repeating decimals