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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. A subset within a field.






2. 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






3. Written as fractions - terminating + repeating decimals






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






5. 3rd. Rule of Complex Arithmetic






6. Any number not rational






7. ? = -tan?






8. A plot of complex numbers as points.






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






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






11. 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.






12. All numbers






13. I^2 =






14. When two complex numbers are multipiled together.






15. Real and imaginary numbers






16. V(x² + y²) = |z|






17. All the powers of i can be written as






18. 1






19. 3






20. Numbers on a numberline






21. 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.






22. A + bi






23. 2ib






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






25. 2a






26. 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






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






28. Imaginary number

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






30. 1






31. z1z2* / |z2|²






32. V(zz*) = v(a² + b²)






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

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






35. 1






36. Divide moduli and subtract arguments






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






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






39. Where the curvature of the graph changes






40. Multiply moduli and add arguments






41. Starts at 1 - does not include 0






42. When two complex numbers are divided.






43. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






44. I






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

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46. When two complex numbers are added together.






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






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






49. To simplify the square root of a negative number






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







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