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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. 1st. Rule of Complex Arithmetic






2. 2ib






3. 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.






4. I






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






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






7. (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






8. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






9. 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






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






11. I^2 =






12. 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






13. All the powers of i can be written as






14. ½(e^(iz) + e^(-iz))






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






16. 2nd. Rule of Complex Arithmetic

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17. A² + b² - real and non negative






18. y / r






19. 1






20. 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






21. Any number not rational






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






23. V(zz*) = v(a² + b²)






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






25. A+bi






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






27. R^2 = x






28. x / r






29. 1






30. The reals are just the






31. Derives z = a+bi






32. To simplify the square root of a negative number






33. A subset within a field.






34. A + bi






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






36. V(x² + y²) = |z|






37. Starts at 1 - does not include 0






38. 5th. Rule of Complex Arithmetic






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






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






41. 1






42. 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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43. The field of all rational and irrational numbers.






44. ? = -tan?






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. z1z2* / |z2|²






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






48. The square root of -1.






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






50. 1







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