Complex NumbersHard
Question
Let ω = - 
then value of the determinant 
is
then value of the determinant is Options
A.3ω
B.3ω (ω- 1)
C.3ω2
D.3ω(1 - ω)
Solution
Let ᐃ = 
Applying R2 → R2 - R1 ; R3 → R3 - R1
= (-2 - ω2)(ω - 1) - (ω2 - 1)2
= 2ω + 2 - ω3 + ω2 - 2(ω4 - ω2 + 1)
= 3ω2 - ω = 3ω(ω - 1) (∵ω4 = ω)
Applying R2 → R2 - R1 ; R3 → R3 - R1
= (-2 - ω2)(ω - 1) - (ω2 - 1)2
= 2ω + 2 - ω3 + ω2 - 2(ω4 - ω2 + 1)
= 3ω2 - ω = 3ω(ω - 1) (∵ω4 = ω)
Create a free account to view solution
View Solution FreeMore Complex Numbers Questions
On the arg and plane, let α = -2 + 3z , β = -2 - 3z & | z | = 1. Then the correct statement is -...For two unimodular complex numbers z1 and z2, if A = and B = , then A-1.B-1 is equal to -...Which of the following complex numbers lies along the angle bisectors of the line -L1 : z = ( 1 + 3λ) + i(1 + 4_...The length of a straight line segment joining complex numbers 2 and −3i is -...The square root of −5 −12i is -...