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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. ? = -tan?






2. 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






3. 2ib






4. All numbers






5. 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






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






7. When two complex numbers are divided.






8. Imaginary number

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






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






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






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






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






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






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






16. x / r






17. 2nd. Rule of Complex Arithmetic

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18. 1






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






20. All the powers of i can be written as






21. (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






22. Any number not rational






23. Root negative - has letter i






24. 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






25. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






26. Any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.






27. 1






28. (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






29. 3






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






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






32. Starts at 1 - does not include 0






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






34. z1z2* / |z2|²






35. 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






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






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






38. E ^ (z2 ln z1)






39. A plot of complex numbers as points.






40. A complex number and its conjugate






41. R^2 = x






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






43. Divide moduli and subtract arguments






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






45. 4th. Rule of Complex Arithmetic






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






47. A + bi






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






49. ½(e^(iz) + e^(-iz))






50. When two complex numbers are multipiled together.