JEE Main 2025 (Online) 28th January Evening ShiftQuestion 1
If $\alpha+i\beta$ and $\gamma+i\delta$ are the roots of $x^{2}-(3-2i)x-(2i-2)=0$, $i=\sqrt{-1}$, then $\alpha\gamma+\beta\delta$ is equal to:
Complex Numbers
Solution
$z=1$ is a root ($1-3+2i-2i+2=0$), so the other is $2-2i$ (sum $3-2i$). Then $\alpha\gamma+\beta\delta=1\cdot2+0\cdot(-2)=2$.