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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • 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. (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






2. z1z2* / |z2|²






3. R^2 = x






4. A subset within a field.






5. A complex number and its conjugate






6. 5th. Rule of Complex Arithmetic






7. 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






8. 3






9. 1






10. Where the curvature of the graph changes






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






12. 1. i^2 = -1 2. Every complex number has the 'Standard Form': a + bi for some real a and b. 3. For real a and b - a + bi = 0 if and only if a = b = 0 4. (a + bi) = (c + bi) = (a + c) + ( b + d)i 5. (a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc






13. A² + b² - real and non negative






14. 2a






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. Real and imaginary numbers






17. ? = -tan?






18. The field of all rational and irrational numbers.






19. When two complex numbers are multipiled together.






20. R?¹(cos? - isin?)






21. A plot of complex numbers as points.






22. When two complex numbers are divided.






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






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






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






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






27. The reals are just the






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






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






30. To simplify a complex fraction






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

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






33. 4th. Rule of Complex Arithmetic






34. Like pi






35. I^2 =






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






37. Have radical






38. All numbers






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

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40. 1st. Rule of Complex Arithmetic






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






42. To simplify the square root of a negative number






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






44. Derives z = a+bi






45. 1






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






47. Multiply moduli and add arguments






48. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.






49. ½(e^(iz) + e^(-iz))






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







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