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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.
  • 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. Root negative - has letter i






2. Rotates anticlockwise by p/2






3. R^2 = x






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






5. The field of all rational and irrational numbers.






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






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






8. The field of numbers of the form - where and are real numbers and i is the imaginary unit equal to the square root of - . When a single letter is used to denote a complex number - it is sometimes called an 'affix.'






9. 5th. Rule of Complex Arithmetic






10. 3rd. Rule of Complex Arithmetic






11. Multiply moduli and add arguments






12. A complex number and its conjugate






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






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






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






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. R?¹(cos? - isin?)






18. When two complex numbers are divided.






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






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






21. The reals are just the






22. All the powers of i can be written as






23. Where the curvature of the graph changes






24. 1






25. 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.

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26. (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






27. x / r






28. 2ib






29. (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






30. Not on the numberline






31. 2a






32. 4th. Rule of Complex Arithmetic






33. V(x² + y²) = |z|






34. 1






35. 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.






36. I






37. Derives z = a+bi






38. y / r






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






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






41. The complex number z representing a+bi.






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






43. V(zz*) = v(a² + b²)






44. z1z2* / |z2|²






45. 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






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






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






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






49. 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






50. Like pi