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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. ½(e^(-y) +e^(y)) = cosh y






2. When two complex numbers are divided.






3. I






4. I^26/4= i^24 x i^2 =-1 so u divide the number by 4 and whatevers left over is the number that its equal to.






5. 1st. Rule of Complex Arithmetic






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






7. All numbers






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






9. Divide moduli and subtract arguments






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






11. 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.'






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






13. E ^ (z2 ln z1)






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






15. No i






16. 2ib






17. 3rd. Rule of Complex Arithmetic






18. 1






19. A+bi






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






21. Numbers on a numberline






22. 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






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






24. R^2 = x






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






26. 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






27. A + bi






28. 2nd. Rule of Complex Arithmetic


29. R?¹(cos? - isin?)






30. 2a






31. The field of all rational and irrational numbers.






32. ½(e^(iz) + e^(-iz))






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






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






35. Where the curvature of the graph changes






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






37. 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.






38. Imaginary number


39. I






40. (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






41. To simplify a complex fraction






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






43. Any number not rational






44. V(zz*) = v(a² + b²)






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






46. I^2 =






47. To simplify the square root of a negative number






48. 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






49. 1






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