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If (√3 + i )^n = (√3- i)^n , n € N , then least value of n is

If (√3 + i )^n = (√3- i)^n , n € N , then least value of n is

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1 Answers

Arun
25750 Points
6 years ago
Dear Kavit
 
On dividing by 2^n both the sides
 
(Cos 30+ i sin30)^n = (cos (-30) + i sin(-30))^n
 
cos (30n) + i sin (30 n) = cos (30n) + i sin(-30 n)
Now
Sin (30 n) = - sin (30n)
2 sin (30n) = 0
Sin(30n) = sin 180°
30 n = 180
 Hence
n = 6
 
 
Regards
Arun (askIITians forum Expert)

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