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






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






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






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






5. ½(e^(-y) +e^(y)) = cosh y






6. The field of all rational and irrational numbers.






7. z1z2* / |z2|²






8. Not on the numberline






9. 1






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






11. Imaginary number

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12. A complex number and its conjugate






13. 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






14. The square root of -1.






15. (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






16. ½(e^(iz) + e^(-iz))






17. A² + b² - real and non negative






18. 2a






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






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






21. Rotates anticlockwise by p/2






22. When two complex numbers are multipiled together.






23. 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






24. 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






25. Where the curvature of the graph changes






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

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






28. Real and imaginary numbers






29. 1






30. The reals are just the






31. 4th. Rule of Complex Arithmetic






32. When two complex numbers are divided.






33. I^26/4= i^24 x i^2 =-1 so u divide the number by 4 and whatevers left over is the number that its equal to.






34. 5th. Rule of Complex Arithmetic






35. I






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






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






38. A subset within a field.






39. The complex number z representing a+bi.






40. V(zz*) = v(a² + b²)






41. All numbers






42. 1






43. 1






44. I






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






46. When two complex numbers are added together.






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






48. 1st. Rule of Complex Arithmetic






49. 3






50. 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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