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KCET2009MathematicsComplex Number

The smallest positive integral value of n such that [ 1+ 8 +i 8 1+ 8 -i 8 ]^ n n is equal to

Options

  1. A4
  2. B3
  3. C2
  4. D8

Correct answer

A. 4

Step-by-step solution

[ 1+ 8 +i 8 1+ 8 -i 8 ]^ n = [ 1+ +i 1+ -i ]^ n ( . Put . = 2 - 8 )= [ 2 ² 2 +2 i 2 2 2 ² 2 -2 i 2 2 ]= [ 2 +i 2 2 -i 2 ]^ n = (e^ 2 i 2 )^ n =e^ i n = e ^ in ( 3 8 ) = 3 n 8 + i 3 n 8 For n=4 , we get imaginary part.

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