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AP EAMCET202120 Aug 2021Morning ShiftMathematicsMatricesActual

If z 1 = 2 + 3 i , z 2 = 3 + 2 i where i = - 1 then z 1 z 2 - z 2 ¯ z 1 ¯ z 1 ¯ - z 2 z 2 ¯ z 1 =

Options

  1. A13 I
  2. BI
  3. C26 I
  4. DZero matrix

Correct answer

C. 26 I

Step-by-step solution

z 1 = 2 + 3 i   ∴   z 1 = 2 - 3 i z 2 = 3 + 2 i   ∴   z 2 = 3 - 2 i Now, z 1 z 2 - z 2 ¯ z 1 ¯ z 1 ¯ - z 2 z 2 ¯ z 1 = z 1 z 1 ¯ + z 2 z 2 ¯ - z 1 z 2 + z 1 z 2 - z 1 z 2 + z 1 z 2 z 1 z 1 ¯ + z 2 z 2 ¯ = ( 2 + 3 i ) ( 2 - 3 i )   +   ( 3 - 2 i ) ( 3 + 2 i ) 0 0 ( 2 + 3 i ) ( 2 - 3 i )   +   ( 3 - 2 i ) ( 3 + 2 i ) = 4 - 9 i 2 + 9 - 4 i 2 0 0 4 - 9 i 2 + 9 - 4 i 2 = 26 0 0 26 = 26 1 0 0 1   =   26 I   ∵

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