Complex Numbers 5 Question 6

6. If ω(1) be a cube root of unity and (1+ω2)n=(1+ω4)n, then the least positive value of n is

(a) 2

(b) 3

(c) 5

(d) 6

(2004, 1M)

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Answer:

Correct Answer: 6. (b)

Solution:

  1. Given, (1+ω2)n=(1+ω4)n
(ω)n =(ω2)n [ω3=1 and 1+ω+ω2=0]
ωn =1
n =3 is the least positive value of n.


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