Search any question & find its solution
Question:
Answered & Verified by Expert
$$
(-1+i \sqrt{3})^{60}=
$$
Options:
(-1+i \sqrt{3})^{60}=
$$
Solution:
1281 Upvotes
Verified Answer
The correct answer is:
$2^{60}$
Here, $(-1+i \sqrt{3})^{60}$
$$
\begin{array}{lrl}
& =2^{60}\left[-\frac{1}{2}+i \frac{\sqrt{3}}{2}\right]^{60} & \\
& =2^{60} \times \omega^{60} & {\left[\because \omega=-\frac{1}{2}+i \frac{\sqrt{3}}{2}\right]} \\
& =2^{60} \times\left(\omega^3\right)^{20} & {\left[\because \omega^3=1\right]} \\
& =2^{60} & {\left[\because \omega^6\right.}
\end{array}
$$
$$
\begin{array}{lrl}
& =2^{60}\left[-\frac{1}{2}+i \frac{\sqrt{3}}{2}\right]^{60} & \\
& =2^{60} \times \omega^{60} & {\left[\because \omega=-\frac{1}{2}+i \frac{\sqrt{3}}{2}\right]} \\
& =2^{60} \times\left(\omega^3\right)^{20} & {\left[\because \omega^3=1\right]} \\
& =2^{60} & {\left[\because \omega^6\right.}
\end{array}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.