Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 202628 JanuaryEvening Shift

Exam: JEE Main
Year: 2026
Date: 28 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Complex Number

JEE Main 2026 · 28 January · Evening Shift · Mathematics · Complex Number

Let A=\ z ∈ ℂ:|z-2| ≤ 4\ and B=\ z ∈ ℂ:|z-2|+|z+2|=5\ . Then the...

Let

A=\{z \in \mathbb{C}:|z-2| \leqslant 4\} \text{ and }B=\{z \in \mathbb{C}:|z-2|+|z+2|=5\}

. Then the max \left\{\left|z_{1}-z_{2}\right|: z_{1} \in \mathrm{~A}\right. and \left.z_{2} \in \mathrm{~B}\right\} is : $Let A=\ z ∈ ℂ:|z-2| ≤ 4\ and B=\ z ∈ ℂ:|z-2|+|z+2|=5\ . Then the max \ |z_ 1 -z_ 2 |: z_ 1 ∈ ~A. and .z_ 2 ∈ ~B\ is :$

Options

A $\frac{17}{2}$
B8
C9
D $\frac{15}{2}$

Correct answer

A. $\frac{17}{2}$

Step-by-step solution

|z - 2| \leq 4 \Rightarrow (x - 2)^2 + y^2 \leq 16

|z - 2| + |z + 2| = 5 \Rightarrow \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1

\Rightarrow \dfrac{4x^2}{25} + \dfrac{4y^2}{9} = 1

$Let A=\ z ∈ ℂ:|z-2| ≤ 4\ and B=\ z ∈ ℂ:|z-2|+|z+2|=5\ . Then the max \ |z_ 1 -z_ 2 |: z_ 1 ∈ ~A. and .z_ 2 ∈ ~B\ is :$
Maximum value of

|z_1 - z_2| = 6 + \dfrac{5}{2} = \dfrac{17}{2}

Practice Complex Number on Quantrex Academy →

More from Complex Number

The number of values of z ∈ ℂ , satisfying the equations |z-(4+8i)|= 10 and… JEE Main 2026 Let S = \ z ∈ ℂ : z^2 + 6 \,iz - 3 = 0\ . Then ∑ _ z ∈ S z^8 is equal to : JEE Main 2026 Let the set of all values of k ∈ ℝ such that the equation z( z + 2 + i) + k(2 + 3i) = 0… JEE Main 2026 Let z_1, z_2 ∈ ℂ be the distinct solutions of the equation z^2 + 4z - (1 + 12i) = 0 .… JEE Main 2026 Let S=\ z ∈ ℂ: z^2+4z+16=0\ . Then ∑_ z ∈ S |z+ 3 i|^2 is equal to: JEE Main 2026 Let z be a complex number such that |z+2| = |z-2| and ((z+3)/(z-i)) = (π)/(4) . Then… JEE Main 2026 Let the circles C_1 : |z| = r and C_2 : |z - 3 - 4i| = 5 , z ∈ ℂ , be such that C_2 lies… JEE Main 2026 Let x and y be real numbers such that 50((2x)/(1+3i) - (y)/(1-2i)) = 31 + 17i , i = -1 .… JEE Main 2026 Let z be a complex number such that |z-6|=5 and |z+2-6 i|=5 . Then the value of z^ 3 +3… JEE Main 2026 Let z=(1+i)(1+2 i)(1+3 i) …(1+n i) , where i= -1 . If |z|^ 2 =44200 , then n is equal to… JEE Main 2026 If z= 3 2 +(i)/(2), i= -1 , then (z^ 201 -i)^ 8 is equal to JEE Main 2026 Let S=\ z: 3 |2 z-3(1+i)| 7\ be a set of complex numbers. Then _ z ∈ S |(z+(1)/(2)(5+3… JEE Main 2026 Let S=\ z ∈ ℂ: 4 z^ 2 + z =0\ . Then ∑_ z ∈ S |z|^ 2 is equal to: JEE Main 2026 Let α= -1+i 3 2 and β= -1-i 3 2 , i= -1 . If (7-7 α+9 β)^ 20 +(9+7 α-7 β)^ 20 +(-7+9 α+7… JEE Main 2026 Let z be the complex number satisfying |z-5| ≤ 3 and having maximum positive principal… JEE Main 2026 If x^ 2 +x+1=0 , then the value of (x+(1)/(x))^ 4 +(x^ 2 + 1 x^ 2 )^ 4 + (x^ 3 + 1 x^ 3… JEE Main 2026 Full Complex Number list Complex Number JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs