A) 1
B) \[-1\]
C) 0
D) None of these
Correct Answer: C
Solution :
Since \[\alpha \] and \[\beta \] are complex roots of unity, we may write \[\alpha =\omega ,\beta ={{\omega }^{2}}\] Hence, \[{{\alpha }^{4}}+{{\beta }^{28}}+\frac{1}{\alpha \beta }={{\omega }^{4}}+{{({{\omega }^{2}})}^{28}}+\frac{1}{\omega .{{\omega }^{2}}}\] \[=\omega +{{\omega }^{56}}+1=\omega +{{\omega }^{2}}+1=0\]You need to login to perform this action.
You will be redirected in
3 sec