$$ (-1+i \sqrt{3})^{60}= $$

Question

Aicharya · Accepted Answer

Here, $(-1+i \sqrt{3})^{60}$ $ \begin{array}{lrl} & =2^{60}\left[-\frac{1}{2}+i \frac{\sqrt{3}}{2}ight]^{60} & \ & =2^{60} 	imes \omega^{60} & {\left[\because \omega=-\frac{1}{2}+i \frac{\sqrt{3}}{2}ight]} \ & =2^{60} 	imes\left(\omega^3ight)^{20} & {\left[\because \omega^3=1ight]} \ & =2^{60} & {\left[\because \omega^6ight.} \end{array} $

$$ (-1+i \sqrt{3})^{60}= $$

Solution