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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. Any number not rational






2. 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






3. Real and imaginary numbers






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






5. 1






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






7. Divide moduli and subtract arguments






8. I






9. 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






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






11. 1






12. 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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13. For real a and b - a + bi =






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






15. The square root of -1.






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

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17. All the powers of i can be written as






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






19. Root negative - has letter i






20. V(x² + y²) = |z|






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






22. y / r






23. Where the curvature of the graph changes






24. 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






25. 2a






26. zn = (cos? + isin?)n = cosn? + isinn? - For all integers n

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27. I






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






29. Multiply moduli and add arguments






30. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






31. 1






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






33. Starts at 1 - does not include 0






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






35. 1






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






37. Have radical






38. Numbers on a numberline






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






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






41. 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






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






43. V(zz*) = v(a² + b²)






44. A+bi






45. 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






46. Rotates anticlockwise by p/2






47. A complex number and its conjugate






48. R^2 = x






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






50. Equivalent to an Imaginary Unit.