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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. R^2 = x






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






3. Imaginary number

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4. The square root of -1.






5. ? = -tan?






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






7. V(zz*) = v(a² + b²)






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






9. The reals are just the






10. Any number not rational






11. 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.






12. When two complex numbers are added together.






13. 1st. Rule of Complex Arithmetic






14. 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






15. (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






16. A subset within a field.






17. What about dividing one complex number by another? Is the result another complex number? Let's ask the question in another way. If you are given four real numbers a -b -c and d - can you find two other real numbers x and y so that






18. (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






19. Have radical






20. I^2 =






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






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






23. Not on the numberline






24. Real and imaginary numbers






25. x / r






26. Equivalent to an Imaginary Unit.






27. ½(e^(-y) +e^(y)) = cosh y






28. Like pi






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






30. All the powers of i can be written as






31. y / r






32. 1






33. 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.'






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






35. When two complex numbers are divided.






36. 1






37. Numbers on a numberline






38. 5th. Rule of Complex Arithmetic






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






40. 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






41. A complex number and its conjugate






42. A + bi






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






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






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






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






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






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






50. 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