JEE Main 2026 23 January Evening Shift
Exam JEE Main
Year 2026
Date 23 January
Shift Evening Shift
Subject Mathematics
Chapter Complex Number JEE Main 2026 · 23 January · Evening Shift · Mathematics · Complex Number
If z= 3 2 +(i)/(2), i= -1 , then (z^ 201 -i)^ 8 is equal to
If
z = 3 2 + i 2 , i = − 1 z=\frac{\sqrt{3}}{2}+\frac{i}{2}, i=\sqrt{-1} z = 2 3 + 2 i , i = − 1 , then
( z 201 − i ) 8 \left(z^{201}-i\right)^{8} ( z 201 − i ) 8 is equal to
Step-by-step solution
z = 3 2 + i 2 = e i π / 6 z = \frac{\sqrt{3}}{2} + \frac{i}{2} = e^{i\pi/6} z = 2 3 + 2 i = e iπ /6 .
z 201 = e i ⋅ 201 π / 6 = e i ⋅ 33.5 π = e i ( 33 π + π / 2 ) z^{201} = e^{i \cdot 201\pi/6} = e^{i \cdot 33.5\pi} = e^{i(33\pi + \pi/2)} z 201 = e i ⋅ 201 π /6 = e i ⋅ 33.5 π = e i ( 33 π + π /2 ) .
Since
e i ⋅ 33 π = e i π = − 1 e^{i \cdot 33\pi} = e^{i\pi} = -1 e i ⋅ 33 π = e iπ = − 1 , we get
z 201 = − 1 ⋅ e i π / 2 = − i z^{201} = -1 \cdot e^{i\pi/2} = -i z 201 = − 1 ⋅ e iπ /2 = − i .
z 201 − i = − i − i = − 2 i z^{201} - i = -i - i = -2i z 201 − i = − i − i = − 2 i .
( z 201 − i ) 8 = ( − 2 i ) 8 = 2 8 ⋅ i 8 = 256 ⋅ 1 = 256 (z^{201} - i)^8 = (-2i)^8 = 2^8 \cdot i^8 = 256 \cdot 1 = 256 ( z 201 − i ) 8 = ( − 2 i ) 8 = 2 8 ⋅ i 8 = 256 ⋅ 1 = 256 .
Practice Complex Number on Quantrex Academy →
← Previous question 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…Next question → Let S=\ z: 3 |2 z-3(1+i)| 7\ be a set of complex numbers. Then _ z ∈ S |(z+(1)/(2)(5+3…
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 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 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 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
