A) \[1\]
B) 2
C) \[-2\]
D) \[-1\]
Correct Answer: C
Solution :
\[z=\frac{\sqrt{3}+i}{2}\] \[=i\left[ \frac{\sqrt{3}}{2i}+\frac{1}{2} \right]\] \[=i\left[ \frac{1}{2}-\frac{i\sqrt{3}}{2} \right]\] \[=-i\left( -\frac{1}{2}+\frac{i\sqrt{3}}{2} \right)\] \[=-i\omega \] \[{{z}^{69}}={{(-i\omega )}^{69}}\] \[={{(-i)}^{69}}.{{\omega }^{69}}\] \[={{(-1)}^{69}}.i{{({{\omega }^{3}})}^{23}}\] \[={{(-1)}^{23}}=-i\]
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