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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. Starts at 1 - does not include 0






2. 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






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






4. x / r






5. R^2 = x






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






7. All numbers






8. I






9. The reals are just the






10. ½(e^(iz) + e^(-iz))






11. 1






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






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. Root negative - has letter i






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






16. 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.






17. In this amazing number field every algebraic equation in z with complex coefficients






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






19. 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






20. 4th. Rule of Complex Arithmetic






21. V(zz*) = v(a² + b²)






22. The square root of -1.






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






24. Like pi






25. When two complex numbers are added together.






26. R?¹(cos? - isin?)






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






28. 1






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






30. y / r






31. Where the curvature of the graph changes






32. To simplify a complex fraction






33. Have radical






34. 1






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






36. Any number not rational






37. (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






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






39. z1z2* / |z2|²






40. ? = -tan?






41. A plot of complex numbers as points.






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






43. 3rd. Rule of Complex Arithmetic






44. No i






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






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






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






48. 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.'






49. 2a






50. When two complex numbers are divided.







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