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COMEDK2012MathematicsComplex Number

The multiplicative inverse of 3+4 i 4-5 i is

Options

  1. A( -8 25 , 31 25 )
  2. B( -8 25 , -31 25 )
  3. C( 8 25 , -31 25 )
  4. D( -8 25 , 31 5 )

Correct answer

B. ( -8 25 , -31 25 )

Step-by-step solution

3+4 i 4-5 i Now, multiplicative inverse is aligned & 4-5 i 3+4 i 3-4 i 3-4 i =& (4-5 i)(3-4 i) 9+16 =& 12-16 i-15 i+20 i² 25 = -8-31 i 25 = (- 8 25 ,- 31 25 ) aligned

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