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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. R^2 = x






2. ½(e^(iz) + e^(-iz))






3. 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






4. When two complex numbers are divided.






5. The complex number z representing a+bi.






6. To simplify a complex fraction






7. z1z2* / |z2|²






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






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






10. 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.'






11. 1






12. All numbers






13. 3






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






15. 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.






16. A plot of complex numbers as points.






17. 2nd. Rule of Complex Arithmetic

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






19. Rotates anticlockwise by p/2






20. 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






21. Equivalent to an Imaginary Unit.






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






23. A subset within a field.






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






25. A + bi






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






27. Numbers on a numberline






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






29. E ^ (z2 ln z1)






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






31. ? = -tan?






32. No i






33. 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






34. To simplify the square root of a negative number






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






36. 1st. Rule of Complex Arithmetic






37. 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






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






39. 1






40. V(zz*) = v(a² + b²)






41. All the powers of i can be written as






42. (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






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






44. Notice that rules 4 and 5 state that we complex numbers together - we can divide by c + di if c and d are not both zero. But there is a much easier way to do division.

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45. 1






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






47. (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






48. When two complex numbers are added together.






49. A+bi






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

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