JEE Main 2021 (Online) 26th February Morning ShiftQuestion 1
The sum of $162^{\text{th}}$ power of the roots of the equation $x^{3}-2x^{2}+2x-1=0$ is $\_\_\_\_\_\_$ .
Complex Numbers
Answer$3$
Solution
$x^3-2x^2+2x-1=(x-1)(x^2-x+1)$, roots $1,e^{i\pi/3},e^{-i\pi/3}$. $e^{162\cdot i\pi/3}=e^{54\pi i}=1$, likewise for the conjugate. Sum $=1+1+1=3$.