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






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






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






4. Any number not rational






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






6. ½(e^(-y) +e^(y)) = cosh y






7. A + bi






8. 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






9. I






10. ½(e^(iz) + e^(-iz))






11. 1






12. 1






13. Multiply moduli and add arguments






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






15. z1z2* / |z2|²






16. The field of all rational and irrational numbers.






17. To simplify a complex fraction






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






19. (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






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






21. 2ib






22. 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






23. Root negative - has letter i






24. I






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






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






27. 3rd. Rule of Complex Arithmetic






28. 2nd. Rule of Complex Arithmetic

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29. V(x² + y²) = |z|






30. Like pi






31. A complex number and its conjugate






32. 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.'






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






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

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






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






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






38. R^2 = x






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






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

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41. A² + b² - real and non negative






42. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






43. When two complex numbers are multipiled together.






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






45. 5th. Rule of Complex Arithmetic






46. When two complex numbers are divided.






47. The reals are just the






48. 3






49. Where the curvature of the graph changes






50. 4th. Rule of Complex Arithmetic