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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • 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. Given (4-2i) the complex conjugate would be (4+2i)






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






4. No i






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






6. Numbers on a numberline






7. I^2 =






8. Divide moduli and subtract arguments






9. 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






10. The square root of -1.






11. E ^ (z2 ln z1)






12. 2ib






13. Imaginary number

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






15. 1






16. A + bi






17. 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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18. Written as fractions - terminating + repeating decimals






19. Starts at 1 - does not include 0






20. x / r






21. A complex number and its conjugate






22. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






23. The complex number z representing a+bi.






24. Where the curvature of the graph changes






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






26. Not on the numberline






27. To simplify the square root of a negative number






28. A subset within a field.






29. 1






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






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






32. R^2 = x






33. V(zz*) = v(a² + b²)






34. Real and imaginary numbers






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

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36. Root negative - has letter i






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






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






39. y / r






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






41. The field of all rational and irrational numbers.






42. (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






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






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






46. ½(e^(iz) + e^(-iz))






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






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






49. All the powers of i can be written as






50. V(x² + y²) = |z|







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