ω is a complex cube root of unity. Match the items of List-I to the items of List-II.
$List - I (A) ω^{1010} + ω^{2020} (B) (1 + ω - ω^{2}) (1 - ω + ω^{2}) (C) (2 + ω^{2} + ω^{4})^{5} (D) (3 + 5 ω + 3 ω^{2})^{3} List - II (i) 0 (ii) 1 (iii) -1 (iv) 4 (v) 8$
The correct match is

Question

ω is a complex cube root of unity. Match the items of List-I to the items of List-II.

List - I (A) ω^{1010} + ω^{2020} (B) (1 + ω - ω^{2}) (1 - ω + ω^{2}) (C) (2 + ω^{2} + ω^{4})^{5} (D) (3 + 5 ω + 3 ω^{2})^{3} List - II (i) 0 (ii) 1 (iii) -1 (iv) 4 (v) 8

The correct match is

Accepted Answer

Correct answer: C. (c) (A ) ^1010+ ^2020= ^336 3+2+ ^673 3+1 = ( ^3 )^336 ^2+ ( ^3 )^673 = ^2+ =-1 ( ∵ ^3=1) (B )(1- + ^2)(1+ - ^2) ∵(1+ + ^2=0) =(- ^2- ^2) (- - )=(-2 ^2) (-2 )=4 ^3=4 (C )(2+ ^2+ ^4)^5=(2+ ^2+ )^5( ∵1+ + ^2=0) . =(1+1+ + ^2)^5= (1+0 )^5=1 (D )(3+5 +3 ^2)^3=(3+2 +3( + ^2))^5 = (3+2 -3 )^3= (2 )^3=8( ∵ + ^2=1)

$ω is a complex cube root of unity. Match the items of List-I to the items of List-II. List - I (A) ω^{1010} + ω^{2020} (B) (1 + ω - ω^{2}) (1 - ω + ω^{2}) (C) (2 + ω^{2} + ω^{4})^{5} (D) (3 + 5 ω + 3 ω^{2})^{3} List - II (i) 0 (ii) 1 (iii) -1 (iv) 4 (v) 8 The correct match is$

Solution

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