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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • 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. xpressions such as ``the complex number z'' - and ``the point z'' are now






2. The complex number z representing a+bi.






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






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






5. ½(e^(-y) +e^(y)) = cosh y






6. 3rd. Rule of Complex Arithmetic






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






8. I






9. (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






10. 1






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






12. R?¹(cos? - isin?)






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






14. 3






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






16. E ^ (z2 ln z1)






17. 2ib






18. 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






19. Imaginary number

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






21. 1






22. ½(e^(iz) + e^(-iz))






23. A+bi






24. When two complex numbers are added together.






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






26. 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.'






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






28. Not on the numberline






29. 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






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

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31. Where the curvature of the graph changes






32. V(x² + y²) = |z|






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






34. When two complex numbers are multipiled together.






35. R^2 = x






36. 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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37. A plot of complex numbers as points.






38. When two complex numbers are divided.






39. All the powers of i can be written as






40. 1






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






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






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. I^2 =






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






46. No i






47. Real and imaginary numbers






48. 2a






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






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