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Math Help - Perform indicated operation (simplify as a+bi)

  1. #1
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    Perform indicated operation (simplify as a+bi)

    1 + 4i / 1 - i

    Thanks in advance!
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  2. #2
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    Quote Originally Posted by Hapa View Post
    1 + 4i / 1 - i

    Thanks in advance!
    Is it (1 + 4i)/(1 - i), that is, \frac{1 + 4i}{1 - i} ? Please be less ambiguous when you post.
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  3. #3
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    My apologies. Yes, it is as you listed

    (1 + 4i) / (1 - i)
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  4. #4
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    Quote Originally Posted by Hapa View Post
    My apologies. Yes, it is as you listed

    (1 + 4i) / (1 - i)
    Use the difference of two squares a^2-b^2 = (a-b)(a+b)
    and i^2 = -1 to rationalise the denominator

    Spoiler:
    \frac{1+4i}{1-i} \times \frac{1+i}{1+i} = \frac{(1+4i)(1+i)}{(1-i)(1+i)}

    \frac{1+i+4i+4i^2}{1-(i^2)} = \frac{-3+5i}{2} = -1.5+2.5i


    google can actually do your sum XD: Click me
    Last edited by e^(i*pi); April 12th 2009 at 05:30 PM. Reason: adding google link
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