If (√3 + i )^n = (√3- i)^n , n € N , then least value of n is
Kavlit , 8 Years ago
Grade
Algebra> If (√3 + i )^n = (√3- i)^n , n € N , then...
1 Answers
Arun
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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