JEE Main 2026 (Online) 23rd January Morning ShiftQuestion 1
Let $S=\{z:3\le|2z-3(1+i)|\le7\}$ be a set of complex numbers. Then $\min_{z\in S}\left|z+\frac12(5+3i)\right|$ is equal to :
Complex Numbers
Solution
$|2z-3(1+i)|=2|z-\tfrac32(1+i)|$, so $\tfrac32\le|z-c|\le\tfrac72$ with $c=\tfrac32(1+i)$. Point $-\tfrac12(5+3i)$ is at distance $5$ from $c$, outside the annulus, so min $=5-\tfrac72=\tfrac32$.