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






2. Rotates anticlockwise by p/2






3. Any number not rational






4. 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.






5. A + bi






6. When two complex numbers are divided.






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






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






9. V(zz*) = v(a² + b²)






10. A subset within a field.






11. (2+i)(2i-3) you would use the foil methom which is first outter inner last. (2x2i)(2x-3)(ix2i^2)(ix(-3) =i-8






12. x / r






13. No i






14. 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






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






16. Starts at 1 - does not include 0






17. 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






18. Real and imaginary numbers






19. A² + b² - real and non negative






20. Have radical






21. (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






22. ½(e^(iz) + e^(-iz))






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






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






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






26. 2nd. Rule of Complex Arithmetic

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






28. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n






29. The field of all rational and irrational numbers.






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






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

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






33. The complex number z representing a+bi.






34. I = imaginary unit - i² = -1 or i = v-1






35. 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






36. The square root of -1.






37. All the powers of i can be written as






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






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






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






41. When two complex numbers are added together.






42. 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






43. I






44. Root negative - has letter i






45. 1






46. Equivalent to an Imaginary Unit.






47. 1






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






49. I^2 =






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