JEE Main 2026 (Online) 2nd April Evening ShiftQuestion 1
Let the circles $C_1:|z|=r$ and $C_2:|z-3-4i|=5$, $z\in\mathbb{C}$, be such that $C_2$ lies within $C_1$. If $z_1$ moves on $C_1$, $z_2$ moves on $C_2$ and $\min|z_1-z_2|=2$, then $\max|z_1-z_2|$ is equal to :
Complex Numbers
Solution
$C_2$ has centre $3+4i$ (distance 5 from origin) and radius 5, so $C_2$ inside $C_1$ needs $r\ge10$ and $\min|z_1-z_2|=r-(5+5)=2\Rightarrow r=12$. $\max|z_1-z_2|=r+5+5=22$. Option (C).