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






2. When two complex numbers are added together.






3. 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






4. All the powers of i can be written as






5. (2i+3)/(9-i)for the denominator you multiply by the conjugate and what u do to the bottom u have to do to the top then you distribute the bottom then the top then add like terms then you simplify. 21i+25/17






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






7. The complex number z representing a+bi.






8. When two complex numbers are multipiled together.






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






10. 1






11. I






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






13. Written as fractions - terminating + repeating decimals






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






15. 2ib






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






17. Any number not rational






18. A subset within a field.






19. A² + b² - real and non negative






20. 1






21. ? = -tan?






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






23. In this amazing number field every algebraic equation in z with complex coefficients






24. V(x² + y²) = |z|






25. V(zz*) = v(a² + b²)






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






27. A complex number and its conjugate






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






29. Where the curvature of the graph changes






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






31. 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






32. Root negative - has letter i






33. To simplify the square root of a negative number






34. Like pi






35. x / r






36. 2nd. Rule of Complex Arithmetic

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






38. (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






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






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






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






42. 3rd. Rule of Complex Arithmetic






43. A + bi






44. 1






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






46. The square root of -1.






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






48. ½(e^(-y) +e^(y)) = cosh y






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






50. The field of all rational and irrational numbers.