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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. (e^(-y) - e^(y)) / 2i = i sinh y






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






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






4. All the powers of i can be written as






5. Any number not rational






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






7. All numbers






8. I^2 =






9. 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






10. 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.






11. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






13. When two complex numbers are divided.






14. Divide moduli and subtract arguments






15. Like pi






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






17. A complex number and its conjugate






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






19. 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






20. Starts at 1 - does not include 0






21. R^2 = x






22. V(x² + y²) = |z|






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






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






25. 1st. Rule of Complex Arithmetic






26. y / r






27. 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






28. A² + b² - real and non negative






29. 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






30. The complex number z representing a+bi.






31. To simplify the square root of a negative number






32. A subset within a field.






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






34. Imaginary number


35. Equivalent to an Imaginary Unit.






36. 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






37. z1z2* / |z2|²






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






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






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


41. When two complex numbers are multipiled together.






42. ½(e^(iz) + e^(-iz))






43. 1






44. Derives z = a+bi






45. To simplify a complex fraction






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






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






48. 3rd. Rule of Complex Arithmetic






49. The reals are just the






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