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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. 1st. Rule of Complex Arithmetic






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






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






4. Divide moduli and subtract arguments






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






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






7. 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.


8. Have radical






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






10. y / r






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






12. x / r






13. 4th. Rule of Complex Arithmetic






14. For real a and b - a + bi =






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






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






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






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






19. V(x² + y²) = |z|






20. ½(e^(iz) + e^(-iz))






21. 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






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






23. z1z2* / |z2|²






24. I^2 =






25. 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






26. ½(e^(-y) +e^(y)) = cosh y






27. Not on the numberline






28. All numbers






29. E ^ (z2 ln z1)






30. Equivalent to an Imaginary Unit.






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






32. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






34. 3rd. Rule of Complex Arithmetic






35. Where the curvature of the graph changes






36. To simplify the square root of a negative number






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






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






39. 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






40. Real and imaginary numbers






41. ? = -tan?






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. 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






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






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






46. 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






47. When two complex numbers are added together.






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






49. The field of all rational and irrational numbers.






50. Any number not rational