STD 11 - 4.1 complex nubers — JEE कक्षा 11 साइन्स — Question

 $\theta  = {\tan ^{ - 1}}\left( {\frac{{\sqrt 3 }}{{ - 1}}} \right) = \frac{{2\pi }}{3}$

 $\therefore \,z = 2\,\left( {\cos \frac{{2\pi }}{3} + i\sin \frac{{2\pi }}{3}} \right)$

  $\therefore \,\,{(z)^{20}} = {\left[ {2\left( {\cos \frac{{2\pi }}{3} + i\sin \frac{{2\pi }}{3}} \right)} \right]^{20}}$

 $ = {2^{20}}{\left( {\cos \frac{{2\pi }}{3} + i\sin \frac{{2\pi }}{3}} \right)^{20}}$$ = {2^{20}}{\left( { - \frac{1}{2} + i\frac{{\sqrt 3 }}{2}} \right)^{20}}$.