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






2. 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.






3. Like pi






4. 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






5. 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






6. One of the numbers ... --2 --1 - 0 - 1 - 2 - ....






7. z1z2* / |z2|²






8. 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






9. ½(e^(-y) +e^(y)) = cosh y






10. When two complex numbers are added together.






11. 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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12. (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






13. The reals are just the






14. ½(e^(iz) + e^(-iz))






15. All the powers of i can be written as






16. A complex number and its conjugate






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






18. (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






19. V(x² + y²) = |z|






20. 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






21. Imaginary number

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22. A² + b² - real and non negative






23. The field of all rational and irrational numbers.






24. V(zz*) = v(a² + b²)






25. 5th. Rule of Complex Arithmetic






26. Real and imaginary numbers






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






28. I^26/4= i^24 x i^2 =-1 so u divide the number by 4 and whatevers left over is the number that its equal to.






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






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

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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. 1






33. No i






34. A plot of complex numbers as points.






35. When two complex numbers are subtracted from one another.






36. The complex number z representing a+bi.






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






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






39. Equivalent to an Imaginary Unit.






40. Where the curvature of the graph changes






41. When two complex numbers are divided.






42. Numbers on a numberline






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






44. All numbers






45. 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.'






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






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






48. The square root of -1.






49. 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






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