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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. 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






2. 2a






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






4. The field of all rational and irrational numbers.






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






6. No i






7. What about dividing one complex number by another? Is the result another complex number? Let's ask the question in another way. If you are given four real numbers a -b -c and d - can you find two other real numbers x and y so that






8. Numbers on a numberline






9. When two complex numbers are added together.






10. y / r






11. A² + b² - real and non negative






12. Starts at 1 - does not include 0






13. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called






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






15. 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






16. To simplify the square root of a negative number






17. 2ib






18. 1






19. A+bi






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






21. 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






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






23. All numbers






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






25. A subset within a field.






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






27. 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






28. R^2 = x






29. Rotates anticlockwise by p/2






30. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






31. 3rd. Rule of Complex Arithmetic






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

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33. When two complex numbers are multipiled together.






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






35. 4th. Rule of Complex Arithmetic






36. 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






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






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






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






40. 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






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






42. (e^(iz) - e^(-iz)) / 2i






43. Derives z = a+bi






44. ½(e^(iz) + e^(-iz))






45. The complex number z representing a+bi.






46. Equivalent to an Imaginary Unit.






47. Where the curvature of the graph changes






48. 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.






49. 1st. Rule of Complex Arithmetic






50. R?¹(cos? - isin?)