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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. All the powers of i can be written as






2. 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






3. Derives z = a+bi






4. Numbers on a numberline






5. 1






6. Divide moduli and subtract arguments






7. 2ib






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






9. Any number not rational






10. 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.






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






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






13. x / r






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






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






16. Multiply moduli and add arguments






17. Imaginary number

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18. A complex number and its conjugate






19. 4th. Rule of Complex Arithmetic






20. 1st. Rule of Complex Arithmetic






21. In the same way that we think of real numbers as being points on a line - it is natural to identify a complex number z=a+ib with the point (a -b) in the cartesian plane.






22. (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






23. ½(e^(iz) + e^(-iz))






24. ? = -tan?






25. 2nd. Rule of Complex Arithmetic

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26. 1






27. A+bi






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






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






30. 5th. Rule of Complex Arithmetic






31. 1






32. When two complex numbers are added together.






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






34. A subset within a field.






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






36. 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






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

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38. z1z2* / |z2|²






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






40. y / r






41. Real and imaginary numbers






42. The complex number z representing a+bi.






43. V(x² + y²) = |z|






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






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






46. The field of all rational and irrational numbers.






47. Have radical






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






49. E ^ (z2 ln z1)






50. V(zz*) = v(a² + b²)