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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. The product of an imaginary number and its conjugate is






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






3. 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






4. z1z2* / |z2|²






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






6. (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






7. 2a






8. The field of all rational and irrational numbers.






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






10. ? = -tan?






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






12. R^2 = x






13. (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






14. Equivalent to an Imaginary Unit.






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






16. Like pi






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






18. 3






19. V(zz*) = v(a² + b²)






20. All the powers of i can be written as






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






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

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23. Where the curvature of the graph changes






24. E ^ (z2 ln z1)






25. Have radical






26. y / r






27. The square root of -1.






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






29. A² + b² - real and non negative






30. ½(e^(iz) + e^(-iz))






31. All numbers






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






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






34. To simplify the square root of a negative number






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






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






37. 1st. Rule of Complex Arithmetic






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






39. Not on the numberline






40. In the same way that we think of real numbers as being points on a line - it is natural to identify a complex number z=a+ib with the point (a -b) in the cartesian plane.






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

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






43. 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.'






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






45. 1






46. 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






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






48. Any number not rational






49. When two complex numbers are multipiled together.






50. The reals are just the