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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. Like pi






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






3. Multiply moduli and add arguments






4. R^2 = x






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

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






8. Starts at 1 - does not include 0






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






10. 1






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






12. Derives z = a+bi






13. 1






14. ½(e^(iz) + e^(-iz))






15. A subset within a field.






16. 1






17. 1






18. 2nd. Rule of Complex Arithmetic

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19. V(zz*) = v(a² + b²)






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






21. 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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22. 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.






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






24. ½(e^(-y) +e^(y)) = cosh y






25. To simplify a complex fraction






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






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






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

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






30. A complex number and its conjugate






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






32. When two complex numbers are multipiled together.






33. The field of numbers of the form - where and are real numbers and i is the imaginary unit equal to the square root of - . When a single letter is used to denote a complex number - it is sometimes called an 'affix.'






34. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






35. 3






36. 2ib






37. Numbers on a numberline






38. A plot of complex numbers as points.






39. A + bi






40. 4th. Rule of Complex Arithmetic






41. A+bi






42. I






43. 2a






44. Imaginary number

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45. No i






46. 5th. Rule of Complex Arithmetic






47. When you add two complex numbers a + bi and c + di - you get the sum of the real parts and the sum of the imaginary parts: (a + bi) + (c + di) = (a + c) + (b + d)i






48. When two complex numbers are divided.






49. Real and imaginary numbers






50. V(x² + y²) = |z|







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