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






2. 1






3. 4th. Rule of Complex Arithmetic






4. zn = (cos? + isin?)n = cosn? + isinn? - For all integers n

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5. The complex number z representing a+bi.






6. 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






7. Have radical






8. V(x² + y²) = |z|






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






10. Not on the numberline






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






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






13. 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






14. 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.






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






16. Numbers on a numberline






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






18. 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






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






20. x / r






21. 3rd. Rule of Complex Arithmetic






22. The field of all rational and irrational numbers.






23. The modulus of the complex number z= a + ib now can be interpreted as






24. To simplify a complex fraction






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






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






27. Multiply moduli and add arguments






28. 1






29. V(zz*) = v(a² + b²)






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






31. All the powers of i can be written as






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






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






34. I






35. The reals are just the






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






37. A subset within a field.






38. 1st. Rule of Complex Arithmetic






39. 3






40. Divide moduli and subtract arguments






41. I^2 =






42. (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






43. Root negative - has letter i






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






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






46. 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






47. To simplify the square root of a negative number






48. When you subtract two complex numbers a + bi and c + di - you get the difference of the real parts and the difference of the imaginary parts: (a + bi) - (c + di) = (a - c) + (b - d)i






49. 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






50. A complex number and its conjugate