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






2. 2nd. Rule of Complex Arithmetic

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3. 1






4. ½(e^(-y) +e^(y)) = cosh y






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






6. No i






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






8. 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






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






10. Where the curvature of the graph changes






11. 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






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






13. All the powers of i can be written as






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






15. z1z2* / |z2|²






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






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






18. Real and imaginary numbers






19. Root negative - has letter i






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






21. 1






22. 1






23. I^2 =






24. 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






25. Divide moduli and subtract arguments






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






27. Equivalent to an Imaginary Unit.






28. When two complex numbers are multipiled together.






29. All numbers






30. 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






31. V(zz*) = v(a² + b²)






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






33. 1st. Rule of Complex Arithmetic






34. I






35. (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






36. 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.






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






38. 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.






39. 3rd. Rule of Complex Arithmetic






40. Have radical






41. I






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






43. 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.'






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






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






46. To simplify the square root of a negative number






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

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48. Starts at 1 - does not include 0






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






50. A + bi