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






2. To simplify a complex fraction






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






4. xpressions such as ``the complex number z'' - and ``the point z'' are now






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






6. I = imaginary unit - i² = -1 or i = v-1






7. Have radical






8. E ^ (z2 ln z1)






9. 1






10. 4th. Rule of Complex Arithmetic






11. I






12. 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.






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






14. To prove that number field every algebraic equation in z with complex coefficients has a solution we need

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15. To simplify the square root of a negative number






16. ½(e^(iz) + e^(-iz))






17. 3






18. 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






19. Numbers on a numberline






20. The field of all rational and irrational numbers.






21. The complex number z representing a+bi.






22. When two complex numbers are divided.






23. 2ib






24. 3rd. Rule of Complex Arithmetic






25. Like pi






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






27. V(x² + y²) = |z|






28. Equivalent to an Imaginary Unit.






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






30. A subset within a field.






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






32. V(zz*) = v(a² + b²)






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






34. 1






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






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






37. ? = -tan?






38. A² + b² - real and non negative






39. 2nd. Rule of Complex Arithmetic

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40. y / r






41. A+bi






42. All the powers of i can be written as






43. (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






44. Real and imaginary numbers






45. Any number not rational






46. 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.'






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






48. 2a






49. (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






50. When two complex numbers are multipiled together.






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