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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. y / r






2. All numbers






3. 1






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






5. 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.






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


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






8. Rotates anticlockwise by p/2






9. To simplify a complex fraction






10. A + bi






11. To simplify the square root of a negative number






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






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






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






15. No i






16. 3






17. When two complex numbers are multipiled together.






18. 1






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






20. All the powers of i can be written as






21. Divide moduli and subtract arguments






22. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i






23. A+bi






24. E ^ (z2 ln z1)






25. What about dividing one complex number by another? Is the result another complex number? Let's ask the question in another way. If you are given four real numbers a -b -c and d - can you find two other real numbers x and y so that






26. 4th. Rule of Complex Arithmetic






27. 1st. Rule of Complex Arithmetic






28. 5th. Rule of Complex Arithmetic






29. Where the curvature of the graph changes






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






31. 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






32. A subset within a field.






33. 3rd. Rule of Complex Arithmetic






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






35. (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






36. Real and imaginary numbers






37. 2ib






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






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






40. 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






41. I






42. The square root of -1.






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






44. Starts at 1 - does not include 0






45. V(zz*) = v(a² + b²)






46. The complex number z representing a+bi.






47. Derives z = a+bi






48. 2nd. Rule of Complex Arithmetic


49. 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






50. 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.