MCQ
The value of $\left(\frac{-1+i \sqrt{3}}{1-i}\right)^{30}$ is
  • A
    $2^{15} i$
  • B
    $-2^{15}$
  • $-2^{15} i$
  • D
    $6^{5}$

Answer

Correct option: C.
$-2^{15} i$
c
$\left(\frac{-1+i \sqrt{3}}{1-i}\right)^{30}=\left(\frac{2 \omega}{1-i}\right)^{30}$

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

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

$=\frac{2^{30}}{-2^{15} \cdot i ^{15}}$

$=-2^{15} i$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free