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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. 2nd. Rule of Complex Arithmetic

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

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






4. 1






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






6. A complex number and its conjugate






7. No i






8. Starts at 1 - does not include 0






9. Have radical






10. A plot of complex numbers as points.






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

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12. I






13. V(x² + y²) = |z|






14. 2a






15. E ^ (z2 ln z1)






16. In the same way that we think of real numbers as being points on a line - it is natural to identify a complex number z=a+ib with the point (a -b) in the cartesian plane.






17. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






18. ½(e^(-y) +e^(y)) = cosh y






19. 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.






20. Rotates anticlockwise by p/2






21. To simplify the square root of a negative number






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






23. 3rd. Rule of Complex Arithmetic






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






25. 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






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






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






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






29. Root negative - has letter i






30. Derives z = a+bi






31. Divide moduli and subtract arguments






32. 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






33. 1






34. All the powers of i can be written as






35. 4th. Rule of Complex Arithmetic






36. 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






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






38. A + bi






39. R^2 = x






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






41. 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






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






43. When two complex numbers are multipiled together.






44. V(zz*) = v(a² + b²)






45. x / r






46. 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






47. (e^(-y) - e^(y)) / 2i = i sinh y






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






49. The field of all rational and irrational numbers.






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







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