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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. Cos n? + i sin n? (for all n integers)






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






3. Root negative - has letter i






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






5. V(x² + y²) = |z|






6. Derives z = a+bi






7. 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.






8. (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






9. 3rd. Rule of Complex Arithmetic






10. 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






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






12. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called






13. A complex number and its conjugate






14. To simplify the square root of a negative number






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






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






17. 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






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






19. A subset within a field.






20. Any number not rational






21. 1






22. Where the curvature of the graph changes






23. Numbers on a numberline






24. (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






25. We see in this way that the distance between two points z and w in the complex plane is






26. Written as fractions - terminating + repeating decimals






27. ½(e^(-y) +e^(y)) = cosh y






28. I^2 =






29. 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






30. 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.






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






32. Imaginary number

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33. x / r






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






35. Divide moduli and subtract arguments






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






37. 1






38. The square root of -1.






39. Rotates anticlockwise by p/2






40. I






41. Equivalent to an Imaginary Unit.






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






43. 5th. Rule of Complex Arithmetic






44. y / r






45. When two complex numbers are divided.






46. A+bi






47. A² + b² - real and non negative






48. When two complex numbers are added together.






49. Not on the numberline






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