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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. Not on the numberline






2. 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






3. 4th. Rule of Complex Arithmetic






4. All numbers






5. 2ib






6. Written as fractions - terminating + repeating decimals






7. R^2 = x






8. 1






9. 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.






10. xpressions such as ``the complex number z'' - and ``the point z'' are now






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






12. Imaginary number

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13. The modulus of the complex number z= a + ib now can be interpreted as






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






15. ½(e^(-y) +e^(y)) = cosh y






16. 1






17. Formula: z1 · z2 = (a + bi)(c + di) = ac +adi +cbi +bdi² = (ac - bd) + (ad +cb)i - when you multiply a complex number by its conjugate - you get a real number.






18. 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






19. Numbers on a numberline






20. (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






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

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22. 1






23. y / r






24. V(zz*) = v(a² + b²)






25. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






27. (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






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






29. To simplify the square root of a negative number






30. 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






31. Derives z = a+bi






32. Starts at 1 - does not include 0






33. The square root of -1.






34. When two complex numbers are divided.






35. z1z2* / |z2|²






36. Multiply moduli and add arguments






37. 1






38. Like pi






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






40. The complex number z representing a+bi.






41. To simplify a complex fraction






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






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






44. For real a and b - a + bi =






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






46. A² + b² - real and non negative






47. 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






48. Real and imaginary numbers






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






50. 2nd. Rule of Complex Arithmetic

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