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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.
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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. To simplify the square root of a negative number






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






3. 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.






4. 1






5. V(zz*) = v(a² + b²)






6. 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






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






8. ½(e^(iz) + e^(-iz))






9. Derives z = a+bi






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






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






12. A subset within a field.






13. 4th. Rule of Complex Arithmetic






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






15. A² + b² - real and non negative






16. 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.






17. All numbers






18. E ^ (z2 ln z1)






19. 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.






20. A + bi






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






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






23. When two complex numbers are divided.






24. Have radical






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






26. V(x² + y²) = |z|






27. Root negative - has letter i






28. ? = -tan?






29. The reals are just the






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






31. Divide moduli and subtract arguments






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

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33. 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






34. A+bi






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






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






37. When two complex numbers are added together.






38. Any number not rational






39. Like pi






40. (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






41. 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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42. ½(e^(-y) +e^(y)) = cosh y






43. A complex number and its conjugate






44. Rotates anticlockwise by p/2






45. When two complex numbers are multipiled together.






46. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






47. All the powers of i can be written as






48. The field of all rational and irrational numbers.






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






50. 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







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