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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. 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






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






3. Starts at 1 - does not include 0






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






5. ? = -tan?






6. 3rd. Rule of Complex Arithmetic






7. Rotates anticlockwise by p/2






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






9. Notice that rules 4 and 5 state that we complex numbers together - we can divide by c + di if c and d are not both zero. But there is a much easier way to do division.

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10. 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






11. 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






12. Have radical






13. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






14. The complex number z representing a+bi.






15. When two complex numbers are multipiled together.






16. 1






17. Derives z = a+bi






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






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. R^2 = x






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






22. To simplify a complex fraction






23. Imaginary number

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24. 4th. Rule of Complex Arithmetic






25. Not on the numberline






26. R?¹(cos? - isin?)






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






28. ½(e^(iz) + e^(-iz))






29. The square root of -1.






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






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






32. 2a






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






34. 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






35. When two complex numbers are added together.






36. I






37. 2ib






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






39. Written as fractions - terminating + repeating decimals






40. Any number not rational






41. A complex number and its conjugate






42. 1






43. The reals are just the






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

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45. V(zz*) = v(a² + b²)






46. A+bi






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






48. Divide moduli and subtract arguments






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






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






Can you answer 50 questions in 15 minutes?



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