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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. Starts at 1 - does not include 0






2. No i






3. 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.'






4. ½(e^(iz) + e^(-iz))






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






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






7. 4th. Rule of Complex Arithmetic






8. y / r






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






10. Root negative - has letter i






11. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






12. 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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13. 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






14. (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






15. 1st. Rule of Complex Arithmetic






16. Rotates anticlockwise by p/2






17. 1






18. Multiply moduli and add arguments






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






20. x / r






21. Derives z = a+bi






22. Numbers on a numberline






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






24. Divide moduli and subtract arguments






25. 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






26. I






27. Equivalent to an Imaginary Unit.






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






29. I






30. 1






31. A + bi






32. Have radical






33. 2ib






34. When two complex numbers are divided.






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






36. 1






37. Where the curvature of the graph changes






38. 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






39. 1






40. Not on the numberline






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






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






43. Real and imaginary numbers






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






45. Like pi






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

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47. 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






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






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






50. A complex number may be taken to the power of another complex number.