QJEEM20Ma2316: JEE Main 2020 Mathematics - Class 11 JEEM20Ma2316 Solution

Question

Verified Solution • 2025–26 Session moderate

The value of

{\left( {{{ - 1 + i\sqrt 3 } \over {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

Step-by-Step Verified Solution