Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20249 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
9 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Complex Number

JEE Main 2024 · 9 April · Evening Shift · Mathematics · Complex Number

Let z be a complex number such that the real part of (z-2 i)/(z+2...

Let zz be a complex number such that the real part of z−2iz+2i\frac{z-2 i}{z+2 i} is zero. Then, the maximum value of ∣z−(6+8i)∣|z-(6+8 i)| is equal to

Options

  1. A12
  2. B10
  3. C8
  4. D∞\infty

Correct answer

A. 12

Step-by-step solution

z−2iz+2i+z‾+2iz‾−2i=0zz‾−2iz‾−2iz+4(−1)+zz‾+2zi+2zi‾+4(−1)=0⇒2∣z∣2=8⇒∣z∣=2∣z−(6+8i)∣maximum =10+2=12\begin{aligned} & \frac{\mathrm{z}-2 \mathrm{i}}{\mathrm{z}+2 \mathrm{i}}+\frac{\overline{\mathrm{z}}+2 \mathrm{i}}{\overline{\mathrm{z}}-2 \mathrm{i}}=0 \\ & \mathrm{z} \overline{\mathrm{z}}-2 \mathrm{i} \overline{\mathrm{z}}-2 \mathrm{i} \mathrm{z}+4(-1) \\ & +\mathrm{z} \overline{\mathrm{z}}+2 \mathrm{z} i+2 \overline{\mathrm{z} i}+4(-1)=0 \\ & \Rightarrow 2|\mathrm{z}|^2=8 \Rightarrow|\mathrm{z}|=2 \\ & |\mathrm{z}-(6+8 \mathrm{i})|_{\text{maximum }}=10+2=12\end{aligned}
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 2026Let S = \ z ∈ ℂ : z^2 + 6 \,iz - 3 = 0\ . Then ∑ _ z ∈ S z^8 is equal to : JEE Main 2026Let the set of all values of k ∈ ℝ such that the equation z( z + 2 + i) + k(2 + 3i) = 0… JEE Main 2026Let z_1, z_2 ∈ ℂ be the distinct solutions of the equation z^2 + 4z - (1 + 12i) = 0 .… JEE Main 2026Let S=\ z ∈ ℂ: z^2+4z+16=0\ . Then ∑_ z ∈ S |z+ 3 i|^2 is equal to: JEE Main 2026Let z be a complex number such that |z+2| = |z-2| and ((z+3)/(z-i)) = (π)/(4) . Then… JEE Main 2026Let the circles C_1 : |z| = r and C_2 : |z - 3 - 4i| = 5 , z ∈ ℂ , be such that C_2 lies… JEE Main 2026Let x and y be real numbers such that 50((2x)/(1+3i) - (y)/(1-2i)) = 31 + 17i , i = -1 .… JEE Main 2026Let A=\ z ∈ ℂ:|z-2| 4\ and B=\ z ∈ ℂ:|z-2|+|z+2|=5\ . Then the max \ |z_ 1 -z_ 2 |: z_ 1… JEE Main 2026Let 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 2026Let 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 2026If z= 3 2 +(i)/(2), i= -1 , then (z^ 201 -i)^ 8 is equal to JEE Main 2026Let 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 2026Let S=\ z ∈ ℂ: 4 z^ 2 + z =0\ . Then ∑_ z ∈ S |z|^ 2 is equal to: JEE Main 2026Let 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 2026Let z be the complex number satisfying |z-5| ≤ 3 and having maximum positive principal… JEE Main 2026 Full Complex Number list Complex Number JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs