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KCET2014MathematicsThree Dimensional Geometry

If ( ) and ( ) are two different comlex numbers with ( | |=1 ), then ( | - 1- | ) is equal to

Options

  1. A1
  2. B( 11 )
  3. C( 1 2 )
  4. D( -1 )

Correct answer

B. ( 11 )

Step-by-step solution

We have, ( | |=1 ) We know that ( |z|²=(z)( z ) ) Thus, [ array l | - 1- |²= ( - 1- ) ( - 1- ) = ( - 1- ) ( - 1- ) = | - 1- |² ( - 1 - ) since, = array ] and conjugate of ( 1 ) is ( 1 ). So, [ aligned & ( - 1- ) ( - 1- )= ( - )( - ) (1- )(1- ) =& ( - )- ( - ) 1(1- - (1- ) =& - - + 1- - + As &|z|²=(z)( z ) =& | |²- - +| |² 1- - +| |²| |² Given | |=1 =& 1- - +| |² 1- - +| |² 1 = 1- - +| |² 1- - +| |² =1 aligned ]

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