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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+bi






2. All numbers






3. Imaginary number


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






5. (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






6. 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






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






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






9. Rotates anticlockwise by p/2






10. R?¹(cos? - isin?)






11. Real and imaginary numbers






12. I






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






14. 1






15. A subset within a field.






16. A complex number and its conjugate






17. x / r






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






19. Not on the numberline






20. 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.






21. To simplify the square root of a negative number






22. Any number not rational






23. Derives z = a+bi






24. E ^ (z2 ln z1)






25. Starts at 1 - does not include 0






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






27. 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.






28. Where the curvature of the graph changes






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






30. 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.


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






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






33. All the powers of i can be written as






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






35. 2ib






36. 1






37. A² + b² - real and non negative






38. 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






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






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






41. When two complex numbers are added together.






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






43. Divide moduli and subtract arguments






44. Like pi






45. 3






46. V(x² + y²) = |z|






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






48. 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.






49. y / r






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