A) \[\frac{1}{2}-\frac{9}{2}i\]
B) \[\frac{1}{4}-\frac{9}{4}i\]
C) \[\frac{1}{4}+\frac{9}{4}i\]
D) \[\frac{3+2i\sin \theta }{1-2i\sin \theta }\]
Correct Answer: D
Solution :
Here: \[{{1}^{1/3}}=1,\omega ,{{\omega }^{2}}\] \[\therefore \]for the equation\[{{(x-2)}^{3}}+27=0\] \[\Rightarrow \] \[{{(x-2)}^{3}}=-27=-{{3}^{3}}\] \[\Rightarrow \] \[(x-2)=-3{{(1)}^{1/3}}\] \[\Rightarrow \] \[(x-2)=-3,-3\omega ,-3{{\omega }^{2}}\] \[\Rightarrow \] \[x=-1,2-3\omega ,2-3{{\omega }^{2}}\]
You need to login to perform this action.
You will be redirected in
3 sec
