JEE Main 2026 — Complex Number Question with Solution

The center of circle $C_1$ is $O_1(0,0)$ and its radius is $r_1=r$.

The center of circle $C_2$ is $O_2(3,4)$ and its radius is $r_2=5$.

The distance between the centers of the two circles is $d=\sqrt{3^2+4^2}=5$.

Since $C_2$ lies entirely within $C_1$, the minimum distance between a point on $C_1$ and a point on $C_2$ is given by $r_1-(d+r_2)$.

We are given that $\min |z_1-z_2|=2$.

$r-(5+5)=2\Rightarrow r-10=2\Rightarrow r=12$

The maximum distance between a point on $C_1$ and a point on $C_2$ is given by $r_1+d+r_2$.

$\max |z_1-z_2|=12+5+5=22$

Answer: $22$