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






2. ? = -tan?






3. (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






4. 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






5. The square root of -1.






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






7. 1st. Rule of Complex Arithmetic






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

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9. 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






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






11. Starts at 1 - does not include 0






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






13. Equivalent to an Imaginary Unit.






14. 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






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






16. Any number not rational






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






18. Written as fractions - terminating + repeating decimals






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






20. 2nd. Rule of Complex Arithmetic

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21. Numbers on a numberline






22. ½(e^(iz) + e^(-iz))






23. The field of all rational and irrational numbers.






24. A + bi = z1 c + di = z2 - addition: z1 + z2 = (a + bi) + (c + di) = (a + c) + (b + d)i subtraction: z1 - z2 = (a - c) + (b - d)i






25. Like pi






26. 5th. Rule of Complex Arithmetic






27. x / r






28. ½(e^(-y) +e^(y)) = cosh y






29. Have radical






30. 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






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






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






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






34. Derives z = a+bi






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






36. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






37. 1






38. Not on the numberline






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






40. 2a






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






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






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






44. 2ib






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

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46. V(x² + y²) = |z|






47. Root negative - has letter i






48. A plot of complex numbers as points.






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






50. 3rd. Rule of Complex Arithmetic







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