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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. 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






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






3. When two complex numbers are multipiled together.






4. 1






5. 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






6. Written as fractions - terminating + repeating decimals






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






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






9. To simplify the square root of a negative number






10. Like pi






11. A subset within a field.






12. 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.






13. 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.






14. Derives z = a+bi






15. E ^ (z2 ln z1)






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






17. A + bi






18. A² + b² - real and non negative






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






20. z1z2* / |z2|²






21. R?¹(cos? - isin?)






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






23. All the powers of i can be written as






24. 2ib






25. 5th. Rule of Complex Arithmetic






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






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

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28. Divide moduli and subtract arguments






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






30. I






31. 1






32. The field of all rational and irrational numbers.






33. V(x² + y²) = |z|






34. Multiply moduli and add arguments






35. When two complex numbers are subtracted from one another.






36. When two complex numbers are divided.






37. 2a






38. 3rd. Rule of Complex Arithmetic






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






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






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






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






43. 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






44. All numbers






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






46. To simplify a complex fraction






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






48. y / r






49. ½(e^(-y) +e^(y)) = cosh y






50. The reals are just the