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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. E ^ (z2 ln z1)






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






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






4. 2ib






5. Starts at 1 - does not include 0






6. A + bi






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






8. Rotates anticlockwise by p/2






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






10. Numbers on a numberline






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






12. 1st. Rule of Complex Arithmetic






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


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






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






16. Like pi






17. 1






18. 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.


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






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






21. 2nd. Rule of Complex Arithmetic


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






23. I






24. Root negative - has letter i






25. I






26. I^2 =






27. For real a and b - a + bi =






28. Real and imaginary numbers






29. V(x² + y²) = |z|






30. V(zz*) = v(a² + b²)






31. 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.






32. ½(e^(iz) + e^(-iz))






33. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






34. 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






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






36. 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.






37. 1






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






39. Where the curvature of the graph changes






40. Divide moduli and subtract arguments






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






42. Multiply moduli and add arguments






43. The square root of -1.






44. (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






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






46. A+bi






47. 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






48. The complex number z representing a+bi.






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


50. 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