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






3. Given (4-2i) the complex conjugate would be (4+2i)






4. R?¹(cos? - isin?)






5. Numbers on a numberline






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






7. 2nd. Rule of Complex Arithmetic


8. 1st. Rule of Complex Arithmetic






9. A² + b² - real and non negative






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






11. When two complex numbers are multipiled together.






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






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






14. Derives z = a+bi






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






16. To simplify a complex fraction






17. R^2 = x






18. 2a






19. 2ib






20. ? = -tan?






21. 3rd. Rule of Complex Arithmetic






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


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






24. Divide moduli and subtract arguments






25. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






26. Rotates anticlockwise by p/2






27. The reals are just the






28. The field of all rational and irrational numbers.






29. Written as fractions - terminating + repeating decimals






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






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






32. A subset within a field.






33. Equivalent to an Imaginary Unit.






34. Real and imaginary numbers






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






36. 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






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






38. 1






39. ½(e^(iz) + e^(-iz))






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


41. A complex number and its conjugate






42. To simplify the square root of a negative number






43. All numbers






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






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


46. The field of numbers of the form - where and are real numbers and i is the imaginary unit equal to the square root of - . When a single letter is used to denote a complex number - it is sometimes called an 'affix.'






47. z1z2* / |z2|²






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






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






50. When two complex numbers are added together.