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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.
  • 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. (a + bi)(c + bi) =






2. The field of all rational and irrational numbers.






3. When two complex numbers are divided.






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






5. 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.






6. 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






7. y / r






8. 3rd. Rule of Complex Arithmetic






9. 3






10. Numbers on a numberline






11. 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.






12. 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






13. When two complex numbers are added together.






14. V(x² + y²) = |z|






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






16. 1






17. V(zz*) = v(a² + b²)






18. I^2 =






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






21. A plot of complex numbers as points.






22. 1






23. z1z2* / |z2|²






24. Equivalent to an Imaginary Unit.






25. The square root of -1.






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






27. 1






28. 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






29. Multiply moduli and add arguments






30. Starts at 1 - does not include 0






31. I






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






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






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


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






36. 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.






37. To simplify the square root of a negative number






38. (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






39. The reals are just the






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






41. The complex number z representing a+bi.






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






43. A subset within a field.






44. Root negative - has letter i






45. A complex number may be taken to the power of another complex number.






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


47. Have radical






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






49. 1st. Rule of Complex Arithmetic






50. E ^ (z2 ln z1)