The value of (-1+i√31-i)^30 is:

Question

The value of $\left(\dfrac{-1+i\sqrt3}{1-i}\right)^{30}$ is:

Accepted Answer

$${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$$

= $${\left( {{{2\omega } \over {1 - i}}} \right)^{30}}$$

= $${{{2^{30}}.{\omega ^{30}}} \over {{{\left( {{{\left( {1 - i} \right)}^2}} \right)}^{15}}}}$$

= $${{{2^{30}}.1} \over {{{\left( {1 + {i^{^2}} - 2i} \right)}^{15}}}}$$

= $${{{2^{30}}.1} \over { - {2^{15}}.{i^{15}}}}$$

= --215i

Solutions · 1