SATHEE: Complex Numbers 5 Question 6

Complex Numbers 5 Question 6

6.

If $ω (\neq 1)$ be a cube root of unity and ${(1 + ω^{2})}^{n} = {(1 + ω^{4})}^{n}$ , then the least positive value of $n$ is

(a) 2

(b) 3

(d) 6

(2004, 1M)

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Answer:

Correct Answer: 6. (b)

Solution:

Given, ${(1 + ω^{2})}^{n} = {(1 + ω^{4})}^{n}$

$\Rightarrow$ $(- ω)^{n}$ $= {(- ω^{2})}^{n}$

$[∵ ω^{3} = 1$ and $1 + ω + ω^{2} = 0]$

$\Rightarrow$ $ω^{n}$ $= 1$

$\Rightarrow$ $n$ $= 3$ is the least positive value of $n$ .

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Complex Numbers 5 Question 6

6.

Answer:

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