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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. x / r






2. 1st. Rule of Complex Arithmetic






3. Any number not rational






4. 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






5. 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






6. R^2 = x






7. Multiply moduli and add arguments






8. 3






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






10. All numbers






11. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






12. 4th. Rule of Complex Arithmetic






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






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






16. Have radical






17. 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






18. 2nd. Rule of Complex Arithmetic

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19. 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






20. A complex number and its conjugate






21. 1






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






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

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24. Equivalent to an Imaginary Unit.






25. A + bi






26. When two complex numbers are added together.






27. A+bi






28. Numbers on a numberline






29. 2ib






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






31. E ^ (z2 ln z1)






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






33. 5th. Rule of Complex Arithmetic






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. I^2 =






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






37. Rotates anticlockwise by p/2






38. No i






39. V(zz*) = v(a² + b²)






40. Imaginary number

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






42. In the same way that we think of real numbers as being points on a line - it is natural to identify a complex number z=a+ib with the point (a -b) in the cartesian plane.






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






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






45. Not on the numberline






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

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






48. Like pi






49. 1






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