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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. I






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






3. 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






4. Imaginary number

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






6. Starts at 1 - does not include 0






7. Root negative - has letter i






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






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






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






11. V(zz*) = v(a² + b²)






12. 2ib






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






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






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






16. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i






17. 1






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






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






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






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






22. Written as fractions - terminating + repeating decimals






23. x / r






24. 1






25. Where the curvature of the graph changes






26. 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






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






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






29. Divide moduli and subtract arguments






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






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






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






33. 1






34. (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






35. ½(e^(-y) +e^(y)) = cosh y






36. E ^ (z2 ln z1)






37. A complex number and its conjugate






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






39. Not on the numberline






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






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






42. E^(i?) = cos? + isin? ; e^(ip) + 1 = 0

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43. All the powers of i can be written as






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






45. V(x² + y²) = |z|






46. 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.






47. 1






48. No i






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






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