# Math Help - complex numbers and synthetic division

1. ## 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!!

2. This ia a start of the first one.
$\frac{1}
{{\left( {2 + i} \right)^4 }} = \frac{{\left( {2 - i} \right)^4 }}
{{5^4 }}$

3. thanks but how did you get 5^4?

4. Originally Posted by ss103
thanks but how did you get 5^4?
$\frac{1}{{z^4 }} = \left( {\frac{{\overline z }}
{{\left| z \right|^2 }}} \right)^4 \quad ,\quad \left| {2 + i} \right|^2 = 5
$