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






2. 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






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






4. A plot of complex numbers as points.






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






6. 1






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






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






9. A + bi






10. 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






11. R?¹(cos? - isin?)






12. 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.'






13. Divide moduli and subtract arguments






14. ½(e^(-y) +e^(y)) = cosh y






15. A+bi






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






17. The field of all rational and irrational numbers.






18. 2ib






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






20. z1z2* / |z2|²






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






22. (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






23. 2a






24. To simplify the square root of a negative number






25. A² + b² - real and non negative






26. 3rd. Rule of Complex Arithmetic






27. 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.






28. I^2 =






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






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 complex number and its conjugate






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






34. y / r






35. I






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






37. Root negative - has letter i






38. The reals are just the






39. No i






40. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






42. All numbers






43. A subset within a field.






44. Like pi






45. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called






46. V(x² + y²) = |z|






47. The square root of -1.






48. 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






49. Have radical






50. Real and imaginary numbers