JEE Main 2020 (Online) 5th September Evening ShiftQuestion 1
The value of $\left(\dfrac{-1+i\sqrt{3}}{1-i}\right)^{30}$ is :
Complex Numbers
Solution
$-1+i\sqrt3=2e^{2\pi i/3}$ and $1-i=\sqrt2e^{-\pi i/4}$, so the ratio is $\sqrt2e^{11\pi i/12}$. Its $30$th power is $2^{15}e^{55\pi i/2}=2^{15}e^{3\pi i/2}=-2^{15}i$.