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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. The complex number z representing a+bi.






2. z1z2* / |z2|²






3. 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.






4. 1






5. V(zz*) = v(a² + b²)






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






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






8. 1






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






10. All the powers of i can be written as






11. R?¹(cos? - isin?)






12. 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






13. E ^ (z2 ln z1)






14. Not on the numberline






15. 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






16. A+bi






17. 4th. Rule of Complex Arithmetic






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






19. 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






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






21. Multiply moduli and add arguments






22. When two complex numbers are added together.






23. To prove that number field every algebraic equation in z with complex coefficients has a solution we need

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24. 1






25. All numbers






26. Any number not rational






27. 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






28. A² + b² - real and non negative






29. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






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






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






32. R^2 = x






33. Like pi






34. A subset within a field.






35. Derives z = a+bi






36. 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






37. Real and imaginary numbers






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






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






40. Starts at 1 - does not include 0






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






42. ½(e^(-y) +e^(y)) = cosh y






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






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






45. When two complex numbers are multipiled together.






46. I






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






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. Has exactly n roots by the fundamental theorem of algebra






50. A + bi