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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. The square root of -1.






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

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






4. The field of all rational and irrational numbers.






5. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






6. 3






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






8. y / r






9. z1z2* / |z2|²






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






11. (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






12. When two complex numbers are added together.






13. All numbers






14. Any number not rational






15. 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






16. (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






17. 2nd. Rule of Complex Arithmetic

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






19. All the powers of i can be written as






20. Real and imaginary numbers






21. 1






22. 1






23. A² + b² - real and non negative






24. Numbers on a numberline






25. 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.'






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






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






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






29. ½(e^(iz) + e^(-iz))






30. Imaginary number

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31. When two complex numbers are multipiled together.






32. 4th. Rule of Complex Arithmetic






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






34. I^2 =






35. Notice that rules 4 and 5 state that we complex numbers together - we can divide by c + di if c and d are not both zero. But there is a much easier way to do division.

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36. A+bi






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






38. A plot of complex numbers as points.






39. I






40. 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






41. Root negative - has letter i






42. To simplify the square root of a negative number






43. Divide moduli and subtract arguments






44. Rotates anticlockwise by p/2






45. A + bi






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






47. V(zz*) = v(a² + b²)






48. To simplify a complex fraction






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






50. 1