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The smallest positive integral value of n for which {1 + i sqrt(3)} ^ n/2 is positive is : a)3 b)6 c)12 d)0 Clearly, {1 + i sqrt(3)} ^ n/2 = (-2)^n/2 * (w)^n/2 therefore, if n=6 then it becomes (-2)^3 which would result in a negative number not positive. Please explain how 6 is the answer. I think 12 will be the answer.

The smallest positive integral value of n for which {1 + i sqrt(3)} ^ n/2 is positive is :
a)3
b)6
c)12
d)0 
Clearly, {1 + i sqrt(3)} ^ n/2 = (-2)^n/2 * (w)^n/2 
 therefore, if n=6 then it  becomes (-2)^3 which would result in a negative number not positive. Please explain how 6 is the answer. I think 12 will be the answer.
 
 

Grade:

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
2^n/2  (– 1)^n/2{ – 1/2  –  i sqrt(3)/2} ^ n/2
 
Now if n = 6
 
This will results in a positive number

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