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Definition of Limit

ω is an imagi...

Question

ω is an imaginary cube root of unity . If $(1 + w^{2})^{m} = (1 + w^{4})^{m}$ , then least positive integral value of m is

A

6

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B

5

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C

4

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D

3

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Solution

The correct option is D 3
We have,
$(1 + w^{2})^{m} = (1 + w^{4})^{m}$ $(∵ w^{3} = 1)$
$(1 + w^{2})^{m} = (1 + w^{4})^{m}$
$(- w)^{m} = (- w^{2})^{m}$
Looking at the options and solving,
Least positive integral value of m is 3.

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ω

is an imaginary cube root of unity. If

(1 + ω^{2})^{m} = (1 + ω^{4})^{m}

then least positive integral value of m is

{(1 + ω^{2})}^{m} = {(1 + ω^{4})}^{m}

ω

is an imaginary cube root of unity, then least positive integral value of

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