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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. (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






2. ½(e^(-y) +e^(y)) = cosh y






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






4. A plot of complex numbers as points.






5. The complex number z representing a+bi.






6. We can also think of the point z= a+ ib as






7. All the powers of i can be written as






8. 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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9. A + bi






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






11. Derives z = a+bi






12. 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






13. Any number not rational






14. 2ib






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. R^2 = x






17. V(zz*) = v(a² + b²)






18. 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.






19. To simplify the square root of a negative number






20. Multiply moduli and add arguments






21. 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






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






23. 1






24. Have radical






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






26. Not on the numberline






27. When two complex numbers are divided.






28. I






29. ½(e^(iz) + e^(-iz))






30. 1st. Rule of Complex Arithmetic






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

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






33. Formula: z1 · z2 = (a + bi)(c + di) = ac +adi +cbi +bdi² = (ac - bd) + (ad +cb)i - when you multiply a complex number by its conjugate - you get a real number.






34. No i






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






36. 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






37. To simplify a complex fraction






38. When two complex numbers are multipiled together.






39. 1






40. 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






41. Numbers on a numberline






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






43. 3






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






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






46. y / r






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






48. Starts at 1 - does not include 0






49. Like pi






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







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