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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. 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






2. Imaginary number

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






4. A² + b² - real and non negative






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






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

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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. For real a and b - a + bi =






9. Numbers on a numberline






10. 3rd. Rule of Complex Arithmetic






11. I






12. Multiply moduli and add arguments






13. All the powers of i can be written as






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. ½(e^(-y) +e^(y)) = cosh y






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






17. Equivalent to an Imaginary Unit.






18. A complex number and its conjugate






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






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






21. (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






22. 3






23. 5th. Rule of Complex Arithmetic






24. All numbers






25. A + bi






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






27. Not on the numberline






28. The field of all rational and irrational numbers.






29. To simplify the square root of a negative number






30. To simplify a complex fraction






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






32. 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






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






34. (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






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






36. Derives z = a+bi






37. When two complex numbers are divided.






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






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






40. Any number not rational






41. 1






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






43. The reals are just the






44. 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






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






46. E ^ (z2 ln z1)






47. I = imaginary unit - i² = -1 or i = v-1






48. 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.






49. Divide moduli and subtract arguments






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