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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. y / r






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






3. All numbers






4. Have radical






5. x / r






6. (e^(-y) - e^(y)) / 2i = i sinh y






7. No i






8. The reals are just the






9. 4th. Rule of Complex Arithmetic






10. V(x² + y²) = |z|






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






12. Equivalent to an Imaginary Unit.






13. I^2 =






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






15. 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






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






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






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






19. 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






20. Multiply moduli and add arguments






21. E ^ (z2 ln z1)






22. ½(e^(-y) +e^(y)) = cosh y






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






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






25. The complex number z representing a+bi.






26. Root negative - has letter i






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






28. 5th. Rule of Complex Arithmetic






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






30. The square root of -1.






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






32. 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






33. 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






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






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






36. 3rd. Rule of Complex Arithmetic






37. A+bi






38. Not on the numberline






39. 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






40. ? = -tan?






41. Rotates anticlockwise by p/2






42. To simplify a complex fraction






43. When two complex numbers are multipiled together.






44. I






45. R?¹(cos? - isin?)






46. Starts at 1 - does not include 0






47. A + bi






48. 1






49. A subset within a field.






50. 2nd. Rule of Complex Arithmetic