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The value of $${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$$ is :

JEE · Math · previous-year question

  1. A.–215icorrect
  2. B.–215
  3. C.215i
  4. D.65

Answer

A. –215i

Explanation

$${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$$ = $${\left( {{{2\omega } \over {1 - i}}} \right)^{30}}$$ = $${{{2^{30}}.{\omega ^{30}}} \over {{{\left( {{{\left( {1 - i} \right)}^2}} \right)}^{15}}}}$$ = $${{{2^{30}}.1} \over {{{\left( {1 + {i^{^2}} - 2i} \right)}^{15}}}}$$ = $${{{2^{30}}.1} \over { - {2^{15}}.{i^{15}}}}$$ = –215i

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