The value of ${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$ is :
Solution
${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$
<br><br>= ${\left( {{{2\omega } \over {1 - i}}} \right)^{30}}$
<br><br>= $${{{2^{30}}.{\omega ^{30}}} \over {{{\left( {{{\left( {1 - i} \right)}^2}} \right)}^{15}}}}$$
<br><br>= ${{{2^{30}}.1} \over {{{\left( {1 + {i^{^2}} - 2i} \right)}^{15}}}}$
<br><br>= ${{{2^{30}}.1} \over { - {2^{15}}.{i^{15}}}}$
<br><br>= –2<sup>15</sup>i
About this question
Subject: Mathematics · Chapter: Complex Numbers and Quadratic Equations · Topic: Modulus and Argument
This question is part of PrepWiser's free JEE Main question bank. 223 more solved questions on Complex Numbers and Quadratic Equations are available — start with the harder ones if your accuracy is >70%.