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COMEDK2013MathematicsBinomial Theorem

The smallest positive integer n for which (1+i)^ 2 n =(1-i)^ 2 n is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

B. 2

Step-by-step solution

We have, aligned & &(1+i)^ 2 n =(1-i)^ 2 n & & ( 1+i 1-i )^ 2 n =1 & & ( 1+i 1-i 1+i 1+i )^ 2 n =1 & & ( 1+i²+2 i 1-i² )^ 2 n &=1 & & ( 1-1+2 i 1+1 )^ 2 n &=1 & & i^ 2 n &=1 & & 2 n &=4 & n &=2 aligned

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