Let the circle \(\mathrm{C}_{1}:|\mathrm{z}|=\mathrm{r}\) and \(\mathrm{C}_{2}:|\mathrm{z}-3-4 \mathrm{i}|=5, \mathrm{z} \in \mathbb{C}\), be such that \(\mathrm{C}_{2}\) lies within \(\mathrm{C}_{1}\). If \(\mathrm{z}_{1}\) moves on \(\mathrm{C}_{1}\), \(\mathrm{z}_{2}\) moves on \(\mathrm{C}_{2}\) and \(\min \left|\mathrm{z}_{1}-\mathrm{z}_{2}\right|=2\), then max \(\left|z_{1}-z_{2}\right|\) is equal to :-

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Complex Numbers

Let the circle

C_{1} : ∣ z ∣ = r

and

C_{2} : ∣ z - 3 - 4 i ∣ = 5, z \in 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 :-

Answer: (C)

C_{1}

is centred at the origin with radius

r

, while

C_{2}

is centred at

3 + 4 i

(a distance

∣3 + 4 i ∣ = 5

from the origin) with radius

5

. With

C_{2}

inside

C_{1}

, the least value of

∣ z_{1} - z_{2} ∣

r - (5 + 5) = r - 10

; setting

r - 10 = 2

gives

r = 12

. The greatest value of

∣ z_{1} - z_{2} ∣

r + (5 + 5) = r + 10 = 22

JEE Main · 2026 · 02 Apr 2026 · Shift 2 · Single correct option