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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. Multiply moduli and add arguments






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






3. 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.






4. To simplify the square root of a negative number






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






6. 2nd. Rule of Complex Arithmetic

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7. x / r






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






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






10. Numbers on a numberline






11. The complex number z representing a+bi.






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






13. (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






14. 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.






15. A + bi = z1 c + di = z2 - addition: z1 + z2 = (a + bi) + (c + di) = (a + c) + (b + d)i subtraction: z1 - z2 = (a - c) + (b - d)i






16. I^2 =






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






18. 4th. Rule of Complex Arithmetic






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

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20. V(x² + y²) = |z|






21. Have radical






22. To simplify a complex fraction






23. Starts at 1 - does not include 0






24. Every complex number has the 'Standard Form':






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






26. 1






27. When two complex numbers are added together.






28. Root negative - has letter i






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

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






31. 3






32. ½(e^(iz) + e^(-iz))






33. A + bi






34. When you add two complex numbers a + bi and c + di - you get the sum of the real parts and the sum of the imaginary parts: (a + bi) + (c + di) = (a + c) + (b + d)i






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






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






37. A subset within a field.






38. 1






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






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






41. A² + b² - real and non negative






42. When two complex numbers are multipiled together.






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






44. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






45. A plot of complex numbers as points.






46. R?¹(cos? - isin?)






47. Real and imaginary numbers






48. The square root of -1.






49. 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.'






50. 3rd. Rule of Complex Arithmetic