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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.
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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. (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






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






3. x / r






4. (2i+3)/(9-i)for the denominator you multiply by the conjugate and what u do to the bottom u have to do to the top then you distribute the bottom then the top then add like terms then you simplify. 21i+25/17






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






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






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






8. 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.






9. A+bi






10. A subset within a field.






11. Numbers on a numberline






12. Like pi






13. 5th. Rule of Complex Arithmetic






14. When two complex numbers are added together.






15. E ^ (z2 ln z1)






16. 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






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






18. A plot of complex numbers as points.






19. 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.


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






21. Derives z = a+bi






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






23. 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






24. 1






25. Equivalent to an Imaginary Unit.






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






27. Where the curvature of the graph changes






28. I






29. 1






30. Multiply moduli and add arguments






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. 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.






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






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






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






36. Imaginary number


37. Any number not rational






38. We see in this way that the distance between two points z and w in the complex plane is






39. 2a






40. Not on the numberline






41. To simplify the square root of a negative number






42. ½(e^(-y) +e^(y)) = cosh y






43. 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.






44. A + bi






45. Real and imaginary numbers






46. ? = -tan?






47. z1z2* / |z2|²






48. V(x² + y²) = |z|






49. 1






50. We consider the a real number x to be the complex number x+ 0i and in this way we can think of the real numbers as a subset of