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  • $\begingroup$ I dont understand,The radix 4 algorithm uses 2nth root of unity as its input but i only know its nth root,Also Why would u change the field? $\endgroup$ Commented Sep 1 at 5:33
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    $\begingroup$ Because you do not have a $2n$th root of unity in $\mathbb F_q$ you must change to a field where you do. In this case $\mathbb F_{q^2}$ has a $2n$th root of unity which we write as $\omega$. $\endgroup$ Commented Sep 1 at 8:02