find the smallest positive integer n for which (1+i)^2n =(1-i)^2n

 (1+i)^2n =(1-i)^2n

((1+i)/(1-i))2n =1

(2i/2)2n =1  [by taking conjugate]

(-1)n=1

therefore minimum value of n is 2

  • 17

2 is the answer

  • -4
1 is the answer
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2
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2
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02
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(1+i)^2n = (1-i)^2n [(1+i)^2]^n =[(1-i)^2]^n (2i)^n =(-2i)^n (2i/-2i)^n =1 (-1)^n = 1 Hence n= 2
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