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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.
  • 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. y / r






3. 1






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






5. R^2 = x






6. z1z2* / |z2|²






7. The square root of -1.






8. The complex number z representing a+bi.






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






10. Divide moduli and subtract arguments






11. When two complex numbers are multipiled together.






12. 1st. Rule of Complex Arithmetic






13. Written as fractions - terminating + repeating decimals






14. A subset within a field.






15. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






16. Numbers on a numberline






17. V(zz*) = v(a² + b²)






18. ½(e^(-y) +e^(y)) = cosh y






19. The field of numbers of the form - where and are real numbers and i is the imaginary unit equal to the square root of - . When a single letter is used to denote a complex number - it is sometimes called an 'affix.'






20. 1






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






22. 2ib






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






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






25. 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






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






27. To simplify a complex fraction






28. 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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29. 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






30. 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






31. Derives z = a+bi






32. Any number not rational






33. 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.






34. 2a






35. 3rd. Rule of Complex Arithmetic






36. (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






37. R?¹(cos? - isin?)






38. All numbers






39. 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






40. Multiply moduli and add arguments






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






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






43. 1






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






45. x / r






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






47. No i






48. To simplify the square root of a negative number






49. ? = -tan?






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

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