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If z = 3 − 4 i , then the value of expression z 4 − 3 z 3 + 3 z 2 + 99 z − 95 is equal to

Options

  1. A5
  2. B6
  3. C− 5
  4. D− 4

Correct answer

A. 5

Step-by-step solution

z = 3 − 4 i ⇒ ( z − 3 ) 2 = − 16 ⇒ z 2 − 6 z + 25 = 0 ⇒ z 4 − 3 z 3 + 3 z 2 + 99 z − 95 = ( z 2 + 3 z − 4 ) ( z 2 − 6 z + 25 ) + 5 = ( z 2 + 3 z − 4 ) ( 0 ) + 5 = 5

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