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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. z1z2* / |z2|²






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






3. 3rd. Rule of Complex Arithmetic






4. 1






5. Have radical






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






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






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






9. V(zz*) = v(a² + b²)






10. When two complex numbers are divided.






11. 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






12. A plot of complex numbers as points.






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






14. ? = -tan?






15. 1






16. 2ib






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






18. Divide moduli and subtract arguments






19. The field of all rational and irrational numbers.






20. 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






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






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






23. Numbers on a numberline






24. I^2 =






25. Derives z = a+bi






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






27. 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.'






28. To simplify the square root of a negative number






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






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






31. 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.






32. Starts at 1 - does not include 0






33. I






34. 1






35. 3






36. Rotates anticlockwise by p/2






37. 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.






38. No i






39. 1st. Rule of Complex Arithmetic






40. R^2 = x






41. ½(e^(-y) +e^(y)) = cosh y






42. 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






43. 5th. Rule of Complex Arithmetic






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






45. x / r






46. Where the curvature of the graph changes






47. 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






48. When two complex numbers are added together.






49. 2nd. Rule of Complex Arithmetic

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50. 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