A) \[1-i\sqrt{3}\]
B) \[-1+i\sqrt{3}\]
C) \[i\sqrt{3}\]
D) \[-i\sqrt{3}\]
E) \[1+i\sqrt{3}\]
Correct Answer: C
Solution :
We knows\[-\frac{1}{2}+\frac{i\sqrt{3}}{2}=\omega \] \[\therefore \] \[4+5{{(\omega )}^{334}}+3{{(\omega )}^{365}}\] \[=4+5{{({{\omega }^{3}})}^{111}}.{{\omega }^{1}}+3{{({{\omega }^{3}})}^{121}}.{{\omega }^{2}}\] \[=4+5\omega +3{{\omega }^{2}}\] \[=4+5\left( -\frac{1}{2}+\frac{i\sqrt{3}}{\sqrt{2}} \right)+3\left( -\frac{1}{2}-\frac{i\sqrt{3}}{2} \right)\] \[=4-\frac{5}{2}+\frac{5i\sqrt{3}}{2}-\frac{3}{2}-\frac{3i\sqrt{3}}{2}\] \[=i\sqrt{3}\]
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