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The smallest positive integral value of ...

The smallest positive integral value of n for which `(1+sqrt3i)^(n/2)` is real is

A

3

B

6

C

12

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`(1+sqrt(3)i)^(n//2)=[2{1/2+(isqrt(3))/(2)}]^(n//2)= (-2omega^(2))^(n//2)omega^(n)`
Clearly, `(-2)^(n//2)omega^(n)` is a positive real number if `n=6,12,24,36….` The smallest of these values is 6.
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Section I - Solved Mcqs
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