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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. A subset within a field.






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






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






4. Equivalent to an Imaginary Unit.






5. 2ib






6. The field of all rational and irrational numbers.






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






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






9. 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.






10. V(x² + y²) = |z|






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. Not on the numberline






13. 5th. Rule of Complex Arithmetic






14. (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






15. ½(e^(-y) +e^(y)) = cosh y






16. x / r






17. To simplify a complex fraction






18. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






19. Like pi






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






21. V(zz*) = v(a² + b²)






22. 1






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






24. Divide moduli and subtract arguments






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






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






27. When two complex numbers are added together.






28. A+bi






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






30. 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






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






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






33. Numbers on a numberline






34. A + bi






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






36. 3






37. 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






38. All numbers






39. 1






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






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






42. All the powers of i can be written as






43. 1st. Rule of Complex Arithmetic






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






45. y / r






46. The reals are just the






47. Any number not rational






48. A plot of complex numbers as points.






49. E ^ (z2 ln z1)






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







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