If -1 be a cube root of unity and 1-2n-1-4n- then the least positive value of n is

Name: CENGA - Grade 11 - Mathematics - Complex Numbers - Q268
Uploaded: 2022-07-04T10:36:42+05:30
Description: We have, (1+ω^2)^n=(1+ω^4)^n ⇒(−ω)^n=(1+ω)^n=(−ω^2)^n ⇒ω^n=1 Hence, the least positive value of n is 3. ...

We have, (1+ω^2)^n=(1+ω^4)^n ⇒(−ω)^n=(1+ω)^n=(−ω^2)^n ⇒ω^n=1 Hence, the least positive value of n is 3. ...

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Standard XIII

Mathematics

Square Root of a Complex Number

If ω≠1 be a c...

Question

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

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Solution

The correct option is B $3$
We have,
$(1 + ω^{2})^{n} = (1 + ω^{4})^{n}$

$\Rightarrow (- ω)^{n} = (1 + ω)^{n} = (- ω^{2})^{n}$

$\Rightarrow ω^{n} = 1$

Hence, the least positive value of $n$ is $3$ .

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Square Root of a Complex Number

Standard XIII Mathematics

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

The correct option is B 3We have, (1+ω2)n=(1+ω4)n ⇒(−ω)n=(1+ω)n=(−ω2)n ⇒ωn=1 Hence, the least positive value of n is 3.

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

The correct option is B $3$
We have,
$(1 + ω^{2})^{n} = (1 + ω^{4})^{n}$

$\Rightarrow (- ω)^{n} = (1 + ω)^{n} = (- ω^{2})^{n}$

$\Rightarrow ω^{n} = 1$

Hence, the least positive value of $n$ is $3$ .