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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. V(zz*) = v(a² + b²)






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






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






4. A complex number and its conjugate






5. zn = (cos? + isin?)n = cosn? + isinn? - For all integers n

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6. 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






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






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






9. 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






10. I^2 =






11. 2a






12. Not on the numberline






13. The square root of -1.






14. 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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15. All the powers of i can be written as






16. 3






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






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






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






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






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






22. No i






23. A+bi






24. 1






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






26. 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.






27. 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.'






28. ? = -tan?






29. 1st. Rule of Complex Arithmetic






30. (e^(-y) - e^(y)) / 2i = i sinh y






31. Divide moduli and subtract arguments






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






33. Written as fractions - terminating + repeating decimals






34. (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






35. 1






36. 1






37. Derives z = a+bi






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






39. Numbers on a numberline






40. Equivalent to an Imaginary Unit.






41. A plot of complex numbers as points.






42. 4th. Rule of Complex Arithmetic






43. V(x² + y²) = |z|






44. Starts at 1 - does not include 0






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

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46. 5th. Rule of Complex Arithmetic






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






48. 3rd. Rule of Complex Arithmetic






49. Imaginary number

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50. 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.