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Shuckle

  • one year ago

Write each quotient as a complex number. -2i / 1+i Is -2/-1 and +2i/-1 the correct answer?

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  1. zepdrix
    • one year ago
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    \[\large\rm \frac{-2i}{1+i}\left(\frac{1-i}{1-i}\right)=\frac{-2i-2}{2}\]Hmm, do you understand this step that I applied?

  2. Shuckle
    • one year ago
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    Yes, I understand that you have to multiply the numerator and denominator by the complex conjugate of the denominator. But from doing that I got the numbers\[\frac{ -2+2i^{2}}{ 1-1i+1i-1^{2}}\]

  3. Shuckle
    • one year ago
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    Wow that thing is hard to use. -_-

  4. zepdrix
    • one year ago
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    Woops your denominator is \(\large\rm 1-1i+1i-i^2\)

  5. Shuckle
    • one year ago
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    I don't understand?

  6. Shuckle
    • one year ago
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    Oh I see, the one is an i. But I still don't know what the final solution should be?

  7. zepdrix
    • one year ago
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    So the middle terms cancel out in the denom, ya? :)\[\large\rm \frac{ -2+2i^{2}}{ 1-1i+1i-i^{2}}=\frac{ -2+2i^{2}}{ 1-i^{2}}\]

  8. zepdrix
    • one year ago
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    i^2 is -1, so the negatives give us a +1 in that spot

  9. Shuckle
    • one year ago
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    Yes, and then multiplied to the denominator of +1 give you a negative one on the bottom?

  10. zepdrix
    • one year ago
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    \[\large\rm =\frac{ -2+2(-1)}{ 1-(-1)}\]

  11. zepdrix
    • one year ago
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    No you're not multiplying, you're adding down there.

  12. Shuckle
    • one year ago
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    Oh.

  13. zepdrix
    • one year ago
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    Oh woops that's a 2i for the first term in the numerator :O

  14. zepdrix
    • one year ago
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    \[\large\rm =\frac{ -2i+2(-1)}{ 1-(-1)}\]

  15. Shuckle
    • one year ago
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    So after that it should be -2i -2 over 1?

  16. zepdrix
    • one year ago
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    No, your denominator simplifies to this:\[\large\rm =\frac{ -2i+2(-1)}{ 1+1}\]

  17. Shuckle
    • one year ago
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    because (-1)(-) makes a positive one, right?

  18. zepdrix
    • one year ago
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    ya :)

  19. Shuckle
    • one year ago
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    So then, it'd be -2+2i over 1+1 which will equal -2 +2i over 2, and then I should divide?

  20. Shuckle
    • one year ago
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    So the answer is -1-i?

  21. zepdrix
    • one year ago
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    yayyy good job \c:/

  22. Shuckle
    • one year ago
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    Thank you so much. :3

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