JEE Main 2020 (Online) 4th September Evening ShiftQuestion 1
If $a$ and $b$ are real numbers such that $(2+\alpha)^4=a+b\alpha$, where $\alpha=\frac{-1+i\sqrt3}2$, then $a+b$ is equal to :
Complex Numbers
Solution
$2+\alpha=\frac{3+i\sqrt3}2=\sqrt3e^{i\pi/6}$, so $(2+\alpha)^4=9e^{i2\pi/3}=9\alpha$. Hence $a=0,b=9$ (unique, since $\alpha\notin\mathbb R$), $a+b=9$. Answer: (A).