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

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2. A complex number and its conjugate






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

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4. No i






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






6. 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






7. 3






8. 1






9. 1






10. When two complex numbers are added together.






11. 1






12. 1






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






14. 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






15. The reals are just the






16. Given (4-2i) the complex conjugate would be (4+2i)






17. Written as fractions - terminating + repeating decimals






18. A plot of complex numbers as points.






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






20. ? = -tan?






21. 5th. Rule of Complex Arithmetic






22. I






23. The complex number z representing a+bi.






24. 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






25. 4th. Rule of Complex Arithmetic






26. R^2 = x






27. (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






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






29. When two complex numbers are multipiled together.






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






31. Starts at 1 - does not include 0






32. The square root of -1.






33. Derives z = a+bi






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






35. To simplify a complex fraction






36. A subset within a field.






37. I^2 =






38. When two complex numbers are divided.






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






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. ½(e^(-y) +e^(y)) = cosh y






42. V(x² + y²) = |z|






43. Where the curvature of the graph changes






44. Multiply moduli and add arguments






45. 2ib






46. I






47. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






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






50. V(zz*) = v(a² + b²)






Can you answer 50 questions in 15 minutes?



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