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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. Imaginary number

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2. A subset within a field.






3. No i






4. 3






5. 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






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






7. Starts at 1 - does not include 0






8. ½(e^(iz) + e^(-iz))






9. 5th. Rule of Complex Arithmetic






10. For real a and b - a + bi =






11. 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






12. 1






13. 1






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

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






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






17. Like pi






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






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






20. 2a






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






22. A+bi






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






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






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






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






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






28. The field of all rational and irrational numbers.






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






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






31. 1






32. (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






33. All numbers






34. 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






35. 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






36. Numbers on a numberline






37. When two complex numbers are divided.






38. Any number not rational






39. ? = -tan?






40. Root negative - has letter i






41. R^2 = x






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






43. 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






44. 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






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






46. E ^ (z2 ln z1)






47. Where the curvature of the graph changes






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






50. V(x² + y²) = |z|







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