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Math Help - complex numbers and synthetic division

  1. #1
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    complex numbers and synthetic division

    -Perform the following operation and write the result in standard form (a+bi).

    1/(2+i)^4



    -Also, is synthetic division the only way you can factor f(x)=2x^3+3x^2-20x-21?



    Thank you!!
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  2. #2
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    This ia a start of the first one.
    \frac{1}<br />
{{\left( {2 + i} \right)^4 }} = \frac{{\left( {2 - i} \right)^4 }}<br />
{{5^4 }}
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  3. #3
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    thanks but how did you get 5^4?
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  4. #4
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    Quote Originally Posted by ss103 View Post
    thanks but how did you get 5^4?
    \frac{1}{{z^4 }} = \left( {\frac{{\overline z }}<br />
{{\left| z \right|^2 }}} \right)^4 \quad ,\quad \left| {2 + i} \right|^2  = 5<br />
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