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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. 1






2. ? = -tan?






3. Have radical






4. When two complex numbers are added together.






5. 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






6. y / r






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






8. Like pi






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






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






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






12. All the powers of i can be written as






13. I






14. A complex number and its conjugate






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






16. 1






17. Divide moduli and subtract arguments






18. Written as fractions - terminating + repeating decimals






19. Any number not rational






20. 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






21. R^2 = x






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






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






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






25. 1






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






27. Imaginary number

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28. 1






29. Starts at 1 - does not include 0






30. 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.'






31. The complex number z representing a+bi.






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






33. 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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34. 4th. Rule of Complex Arithmetic






35. R?¹(cos? - isin?)






36. x / r






37. Cos n? + i sin n? (for all n integers)






38. A+bi






39. 2ib






40. To simplify a complex fraction






41. All numbers






42. V(zz*) = v(a² + b²)






43. z1z2* / |z2|²






44. 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






45. ½(e^(-y) +e^(y)) = cosh y






46. 3






47. Numbers on a numberline






48. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






49. 2nd. Rule of Complex Arithmetic

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50. ½(e^(iz) + e^(-iz))






Can you answer 50 questions in 15 minutes?



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