ω is a complex cube root of unity. Match the items of List-I to the items of List-II List-I List-II A) ω 1010 + ω 2000 I) 0 B) 1 + ω - ω 2 1 - ω + ω 2 II) 1 C) 2 + ω 2 + ω 4 5 III) - 1 D) 3 + 5 ω + 3 ω 2 3 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 List-II A) ω 1010 + ω 2000 I) 0 B) 1 + ω - ω 2 1 - ω + ω 2 II) 1 C) 2 + ω 2 + ω 4 5 III) - 1 D) 3 + 5 ω + 3 ω 2 3 IV) 4 V) 8 The correct match is, A B C D III IV I V, A B C D I IV II V, A B C D III IV II V, A B C D III I II IV

MARKS App · Accepted Answer

A ω 1010 + ω 2000 = ω 3 × 336 + 2 + ω 3 × 666 + 2 = ω + ω 2 ∵ ω 3 n + 2 = ω 2 ω 3 n + 1 = ω = - 1 B 1 + ω - ω 2 1 - ω + ω 2 = - ω 2 - ω 2 - ω - ω ∵ 1 + ω + ω 2 = 0 = - 2 ω 2 - 2 ω = 4 ω 3 = 4 C 2 + ω 2 + ω 4 5 = 1 + 1 + ω 2 + ω 5 ω 4 = ω 3 · ω = ω = 1 + 0 5 = 1 D 3 + 5 ω + 3 ω 2 3 = 3 1 + ω 2 + 5 ω 3 = - 3 ω + 5 ω 3 = 2 ω 3 = 8 ω 3 = 8

Search any question & find its solution

Looking for more such questions to practice?

List-I		List-II
A)	$ω^{1010} + ω^{2000}$	I)	$0$
B)	$(1 + ω - ω^{2}) (1 - ω + ω^{2})$	II)	$1$
C)	${(2 + ω^{2} + ω^{4})}^{5}$	III)	$- 1$
D)	${(3 + 5 ω + 3 ω^{2})}^{3}$	IV)	$4$
		V)	$8$